Form of Restricted Stock Units Award Agreement

Exhibit 10.7

RESTRICTED STOCK UNITS AWARD AGREEMENT

THIS RESTRICTED STOCK UNITS AWARD AGREEMENT (this “Agreement”) is made and entered into by and between PetroQuest Energy, Inc., a corporation organized under the laws of the State of Delaware (the “Company”), and [__________] (the “Participant”), an individual, on the 8th day of February, 2019 (the “Grant Date”), pursuant to the PetroQuest Energy, Inc. 2019 Long Term Incentive Plan (the “Plan”). The Plan is incorporated by reference herein in its entirety. Capitalized terms not otherwise defined in this Agreement shall have the meaning given to such terms in the Plan.

WHEREAS, Participant is an Employee, and in connection therewith, the Company desires to grant to Participant the number of restricted stock units identified in this Agreement (“Restricted Stock Units” or “RSUs”), subject to the terms and conditions of this Agreement and the Plan, with a view to increasing Participant’s interest in the Company’s welfare and growth; and

WHEREAS, Participant desires to have the opportunity to be a holder of the RSUs subject to the terms and conditions of this Agreement and the Plan.

NOW, THEREFORE, in consideration of the premises, mutual covenants and agreements contained herein, and other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties hereto, intending to be legally bound hereby, agree as follows:

1. Grant of RSUs. Subject to the restrictions, forfeiture provisions and other terms and conditions set forth herein, the Company hereby grants to Participant [__________] RSUs, which shall entitle Participant to receive the same number of Stock (“Shares”) granted to Participant pursuant to the RSUs that are vested pursuant to Section 2 or 3 of this Agreement on the applicable settlement date specified in Section 4 of this Agreement. This Agreement and its grant of RSUs is subject to the terms and conditions of the Plan, and the terms and conditions of the Plan shall control, except to the extent otherwise permitted or authorized in the Plan and specifically addressed in this Agreement. The Plan and this Agreement shall be administered by the Committee pursuant to the Plan.

2. Vesting Schedule. The RSUs shall become vested as set forth in this Section 2; provided, that, subject to Section 3, Participant then is, and continuously since the Grant Date has been, an Employee.

(a) [__________] RSUs (“Grant Date RSUs”) shall be fully vested as of the Grant Date;

(b) [__________] RSUs (“First Emergence RSUs”) will fully vest on the earliest to occur of: (i) the first anniversary of the Grant Date and (ii) a “Change in Control” (for the purposes of vesting in this Agreement shall mean as defined in the termination agreement between Participant and the Company, or if there is no such definition, as defined in the employment agreement between Participant and the Company, and if neither of the foregoing applies, as defined in the Plan); and

(c) [__________] RSUs (“Second Emergence RSUs”) shall fully vest on the earliest to occur of: (i) the third anniversary of the Grant Date, (ii) a Change in Control, and (iii) the

attainment, following the Grant Date, of a 20-trading day volume-weighted average price of a Share (“VWAP Price”) at least equal to $20.00.

3. Forfeiture/Vesting on Termination. The provisions of this Section 3 shall apply with respect the vesting/forfeiture of RSUs upon termination of the Participant’s employment with the Company. Any RSUs forfeited under this Agreement shall automatically revert to the Company and become canceled.

(a) Grant Date RSUs. The Grant Date RSUs will not be subject to forfeiture on any termination of the Participant’s employment.

(b) First Emergence RSUs. The First Emergence RSUs will become fully vested and non-forfeitable upon any termination of the Participant’s employment prior to the first anniversary of the Grant Date (i) by the Company other than a termination for “Cause,” which shall have for the purposes of this Agreement the meaning of such term in the termination or employment agreement between the Participant and the Company (without regard to any requiring any “change in control” as provided therein), and if neither applies, then as defined in the Plan, (ii) a termination due to Participant’s death or Disability, or (iii) a termination by Participant for “Good Reason,” which shall have the meaning of such term in the termination agreement between Participant and the Company, and if there is no such termination agreement, as defined in the employment agreement between the Company and Participant. The First Emergence RSUs will be forfeited upon any other termination of the Participant’s employment by the Participant prior to the first anniversary of the Grant Date.

(c) Second Emergence RSUs. The Second Emergence RSUs will be forfeited in the event of the termination of the Participant’s employment for any reason prior to vesting; provided, however, that if the Participant’s employment is terminated by the Company due to Disability or in the event of the Participant’s death, the Participant will become vested in the number of Second Emergence RSUs equal to the product of (i) the total number of Second Emergence RSUs granted hereunder, multiplied by (ii) a fraction, the numerator of which is the number of months elapsed from the Grant Date through the date of such termination and the denominator of which is 36.

4. Settlement of RSUs. RSUs, to the extent vested, will be settled through delivery of Shares as follows:

(a) Grant Date RSUs will be settled in Shares on the earlier of (i) the Participant’s termination of employment for any reason, (ii) a “Change in Control,” which for purposes of settlement under this Section 4(a) shall mean as defined in the Participant’s termination agreement or employment agreement with the Company, or if neither applies as defined, under the Plan, or (iii) March 25, 2019;

(b) First Emergence RSUs and Second Emergence RSUs will be settled in Shares at vesting.

5. Tax Requirements.

Tax Withholding. Tax withholding with respect to Shares delivered upon settlement may be paid pursuant to the Participant’s written election either (i) by certified check or wire transfer

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or (ii) through “net” settlement, by having the Company withhold Shares having a Fair Market Value on the date the tax is to be determined equal to at least the minimum statutory total tax which could be imposed on the transaction with any fraction of a Share required to satisfy such obligation to be disregarded and the amount due instead to be paid in cash or its equivalent by the Participant at the Participant’s discretion. In the absence of an election, the Company shall have the power and the right to deduct or withhold, or require the Participant to remit to the Company, an amount sufficient to satisfy federal, state, and local taxes, domestic or foreign, required by law or regulation to be withheld with respect to any taxable event arising as a result of the Plan and this Agreement.

6. Miscellaneous.

(a) Certain Transfers Void. Any purported transfer of Shares or RSUs in breach of any provision of this Agreement or the Plan shall be void and ineffectual, and shall not operate to transfer any interest or title in the purported transferee.

(b) No Fractional Shares. All provisions of this Agreement concern whole Shares. If the application of any provision hereunder would yield a fractional Share, such fractional Share shall be rounded down to the next whole Share if it is less than 0.5 and rounded up to the next whole Share if it is 0.5 or more.

(c) Not an Employment or Service Agreement. This Agreement is not an employment agreement, and this Agreement shall not be, and no provision of this Agreement shall be, construed or interpreted to create any right of Participant to continue employment with or provide services to the Company, its Subsidiaries or any of their affiliates.

(d) Notices. Any notice, instruction, authorization, request or demand required hereunder shall be in writing, and shall be delivered either by personal delivery, by telegram, telex, e-mail, telecopy or similar facsimile means, by certified or registered mail, return receipt requested, or by courier or delivery service, addressed to the Company at the address indicated beneath its signature on the execution page of this Agreement, and to Participant at his address indicated on the Company’s stock records, or at such other address and number as a party shall have previously designated by written notice given to the other party in the manner hereinabove set forth. Notices shall be deemed given when received, if sent by facsimile means (confirmation of such receipt by confirmed facsimile transmission being deemed receipt of communications sent by facsimile means); and when delivered and receipted for (or upon the date of attempted delivery where delivery is refused), if hand-delivered, sent by express courier or delivery service, or sent by certified or registered mail, return receipt requested.

(e) Amendment and Waiver. This Agreement may be amended, modified or superseded only by written instrument executed by the Company and Participant. Any waiver of the terms or conditions hereof shall be made only by a written instrument executed and delivered by the party waiving compliance. Any waiver granted by the Company shall be effective only if executed and delivered by a duly authorized executive officer of the Company other than Participant. The failure of any party at any time or times to require performance of any provisions hereof, shall in no manner effect the right to enforce the same. No waiver by any party of any term or condition, or the breach of any term or condition contained in this Agreement in one or more instances shall be

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deemed to be, or construed as, a further or continuing waiver of any such condition or breach or a waiver of any other condition or the breach of any other term or condition.

(f) Governing Law and Severability. This Agreement shall be governed by the internal laws, and not the laws of conflict, of the State of Delaware. The invalidity of any provision of this Agreement shall not affect any other provision of this Agreement, which shall remain in full force and effect.

(g) Successors and Assigns. Subject to the limitations which this Agreement imposes upon transferability of Shares, this Agreement shall bind, be enforceable by and inure to the benefit of the Company and its successors and assigns, and Participant, and Participant’s permitted assigns and upon death, estate and beneficiaries thereof (whether by will or the laws of descent and distribution), executors, administrators, agents, legal and personal representatives.

(h) Community Property. Each spouse individually is bound by, and such spouse’s interest, if any, in any Shares is subject to, the terms of this Agreement. Nothing in this Agreement shall create a community property interest where none otherwise exists.

(i) Entire Agreement. This Agreement together with the Plan supersede any and all other prior understandings and agreements, either oral or in writing, between the parties with respect to the subject matter hereof and constitute the sole and only agreements between the parties with respect to the said subject matter. All prior negotiations and agreements between the parties with respect to the subject matter hereof are merged into this Agreement. Each party to this Agreement acknowledges that no representations, inducements, promises, or agreements, orally or otherwise, have been made by any party or by anyone acting on behalf of any party, which are not embodied in this Agreement or the Plan and that any agreement, statement or promise that is not contained in this Agreement or the Plan shall not be valid or binding or of any force or effect.

(j) Compliance with Other Laws and Regulations. This Agreement, the grant of RSUs and issuance of Common Stock shall be subject to all applicable federal and state laws, rules, regulations and applicable rules and regulations of any exchanges on which such securities are traded or listed, and Company rules or policies. Any determination in which connection by the Committee shall be final, binding and conclusive on the parties hereto and on any third parties, including any individual or entity.

(k) Independent Legal and Tax Advice. The Participant has been advised and Participant hereby acknowledges that he has been advised to obtain independent legal and tax advice regarding this Agreement, grant of the RSUs and the disposition of such Shares, including, without limitation, the impact of Section 409A of the Code.

7. Counterparts and Electronic Execution. This Agreement may be executed in multiple original counterparts, each of which shall be deemed an original, but all of which together shall constitute but one and the same instrument.

8. No Rights as Stockholder. The Participant shall have no rights as a stockholder with respect to the Shares underlying the RSUs and this Agreement until such RSUs are vested and the shares have been issued to Participant.

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9. Code Section 409A. The Committee shall to the extent applicable interpret and construe this Agreement to comply with Code Section 409A, and to the extent required a Change in Control shall be limited to a Change in Control that complies with Code Section 409A. The Committee may interpret or amend this Agreement to comply with Code Section 409A without the Participant’s consent even if such amendment would have an adverse effect on this Agreement. To the extent required under Code Section 409A, in the case of any Participant who is specified employee, a distribution on account of a separation from service may not be made before the date which is six months after the date of the Participant’s separation from service (or, if earlier, the date of the Participant’s death). For purposes of the foregoing and to the extent required by Code Section 409A with respect to an Agreement, the terms “separation from service” and “specified employee” all shall be defined in the same manner as those terms are defined for purposes of Section 409A of the Code, and the limitations set forth herein shall be applied in such manner (and only to the extent) as shall be necessary to comply with any requirements of Section 409A of the Code that are applicable to the Agreement as determined by the Committee. Furthermore, to the extent required under Code Section 409A, none of the Company, the Committee or Board shall have any discretion otherwise provided in the Plan or herein to the extent such discretion is prohibited under Code Section 409A for compliance with Code Section 409A with respect to deferred compensation including, without limitation, any discretion to accelerate or substitute as permitted under the Plan or determine an event is or is not a Change in Control. Notwithstanding anything in this Agreement or elsewhere to the contrary, a termination of employment shall not be deemed to have occurred for purposes of any provision of this Agreement providing for the payment of any amounts or benefits that constitute “non-qualified deferred compensation” within the meaning of Section 409A upon or following a termination of Participant’s employment unless such termination is also a “separation from service” within the meaning of Section 409A and, for purposes of any such provision of this Agreement, references to a “termination,” “termination of employment” or like terms shall mean “separation from service” and the date of such separation from service shall be the date of termination for purposes of any such payment or benefits. Notwithstanding the foregoing, none of the Company, any Affiliate or any officer, director, employee, shareholder or any agent of any of them guarantees or is responsible for the tax consequences to the Participant with respect to this Agreement under the Plan and the administration of the Plan, including without limitation, any excise or penalty tax or interest under Code Section 409A. Participant is advised to consult Participant’s tax advisor with respect to this Agreement and the tax consequences of this Agreement and any payments hereunder.

10. Participant’s Acknowledgments. The Participant acknowledges receipt of a copy of the Plan and represents that he or she is familiar with the terms and provisions thereof, and hereby accepts this Agreement subject to all the terms and provisions of the Plan and this Agreement. The Participant hereby agrees to accept as binding, conclusive, and final all decisions or interpretations of the Committee or the Board, as appropriate, upon any questions arising under the Plan or this Agreement.

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IN WITNESS WHEREOF, the parties have caused this Agreement to be executed on the date as first set forth above.

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