SECOND AMENDMENT TO THE STONE ENERGY CORPORATION 2009 AMENDED AND RESTATED STOCK INCENTIVE PLAN

Exhibit 10.1

SECOND AMENDMENT TO THE

STONE ENERGY CORPORATION

2009 AMENDED AND RESTATED STOCK INCENTIVE PLAN

THIS SECOND AMENDMENT (this “Second Amendment”) to the Stone Energy Corporation 2009 Amended and Restated Stock Incentive Plan, as amended from time to time (the “Plan”), is made by Stone Energy Corporation (the “Company”).

W I T N E S S E T H:

WHEREAS, the Company previously adopted the Plan, under which the Company is authorized to grant equity-based incentive awards to certain employees and other service providers of the Company;

WHEREAS, Article X of the Plan provides that the Company’s board of directors (the “Board”) may amend the Plan from time to time without approval of the stockholders of the Company, subject to certain exceptions including the requirement that any amendment to the Plan to increase the number of shares of common stock, $0.01 par value per share, of the Company (“Common Stock”) that may be issued under the Plan must be approved by the stockholders of the Company;

WHEREAS, the Board desires to increase the number of shares of Common Stock available under the Plan and to make certain other revisions determined to be advisable by the Chief Executive Officer of the Company; and

WHEREAS, in connection with such approval, the Company hereby adopts this Second Amendment, effective as of May 21, 2015 (the “Effective Date”) and subject to approval by the stockholders of the Company, to (i) increase the number of shares of Common Stock available for issuance under the Plan, (ii) extend the term of the Plan, and (iii) make certain other clarifying changes under the Plan.

NOW, THEREFORE, the Plan shall be amended as of the Effective Date, subject to approval by the Company’s stockholders, as set forth below:

1. Paragraph III of the Plan is hereby amended and restated in its entirety to read as follows:

III. EFFECTIVE DATE AND DURATION OF THE PLAN

The 2004 Plan, the 2001 Plan, the 2000 Plan, and the 1993 Plan were effective on the dates provided therein. The Plan was amended and restated effective and approved by the stockholders of the Company as of May 28, 2009. The Plan was further amended effective May 20, 2011. This Second Amendment shall be effective as of May 21, 2015, provided this Second Amendment is approved by the stockholders of the Company at a duly called meeting of the stockholders (or any adjournment thereof) held on May 21, 2015 (or, if

applicable, on the date of such adjournment). If this Second Amendment is not so approved by the stockholders, then this Second Amendment shall be void ab initio, and the Plan shall continue in effect as if this Second Amendment had not been made. No further Awards may be granted under the Plan after May 21, 2025. The Plan shall remain in effect until all Options granted under the Plan have been satisfied or expired and all Restricted Stock Awards granted under the Plan have vested or been forfeited. No “Bonus Stock Award” (as such term is defined in the 2004 Plan) shall be granted to any individual who was not eligible to receive such award prior to May 28, 2009, under the terms of the 2004 Plan.

2. Subparagraph V(a) of the Plan is hereby amended and restated in its entirety to read as follows:

(a) Shares Subject to the Plan. Subject to adjustment in the same manner as provided in Paragraph IX with respect to shares of Common Stock subject to Options then outstanding, the aggregate number of shares of Common Stock that may be issued under the Plan, and the maximum number of shares of Common Stock that may be issued under the Plan through Incentive Stock Options, shall not exceed 10,125,000 shares (which number includes the number of shares of Common Stock previously issued pursuant to an award (or made subject to an award that has not expired or been terminated) granted under the 2004 Plan, the 2001 Plan, the 2000 Plan, or the 1993 Plan). Shares of Common Stock subject to an Award under this Plan that expires or is canceled, forfeited, exchanged, settled in cash or otherwise terminated without the actual delivery of shares (Restricted Stock Awards shall not be considered “delivered shares” for this purpose), will again be available for Awards under this Plan, except that if any such shares could not again be available for Awards to a particular Participant under any applicable law or regulation, such shares shall be available exclusively for Awards to Participants who are not subject to such limitation. Notwithstanding the foregoing, (i) the number of shares tendered or withheld in payment of any exercise or purchase price of an Award or taxes relating to an Award, (ii) shares that were subject to an Option or a Stock Appreciation Right but were not issued or delivered as a result of the net settlement or net exercise of such Option or Stock Appreciation Right and (iii) shares repurchased on the open market with the proceeds of an Option’s exercise price, will not, in each case, be available for Awards under this Plan. The Board may adopt reasonable counting procedures to ensure appropriate counting, avoid double counting (as, for example, in the case of tandem or substitute Awards) and make adjustments if the number of shares of Common Stock actually delivered differs from the number of shares previously counted in connection with an Award.

3. Except as expressly amended or modified in this Second Amendment, all terms and provisions of the Plan are and shall remain in full force and effect and all references therein to such Plan shall henceforth refer to the Plan as modified by this Second Amendment.

IN WITNESS WHEREOF, the Company has caused the execution of this Second Amendment by its duly authorized officer.