Exhibit 5.1

191 Peachtree Street NE, Suite 849

Atlanta, Georgia 30303
770-282-5111 | FAX: 770-282-3779

April 12, 2022

Origin Bancorp, Inc.

500 South Service Road East

Ruston, Louisiana 71270

Attention: Drake Mills

Ladies and Gentlemen:

We have acted as special counsel to Origin Bancorp, Inc., a Louisiana corporation (the “Company”), in connection with certain legal matters with respect to the preparation and filing of a Registration Statement on Form S-4 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”). The Registration Statement contemplates the offering of up to 6,828,390 shares (the “Shares”) of the Company’s common stock, par value $5.00 per share, pursuant to that certain Agreement and Plan of Merger, dated February 23, 2022 (the “Merger Agreement”), by and between the Company and BT Holdings, Inc. This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K of the General Rules and Regulations of the Securities Act.

In connection with rendering the opinion set forth below, we have examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of (a) the Registration Statement, (b) the Articles of Incorporation of the Company, as amended to date and currently in effect, (c) the Amended and Restated Bylaws of the Company, as amended to date and currently in effect, (d) the Merger Agreement, and (e) certain resolutions of the Board of Directors of the Company relating to the transactions described in the Registration Statement. We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents, certificates and records as we have deemed necessary or appropriate as a basis for the opinion set forth below.

In our examination, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as facsimile, electronic, certified or photostatic copies, the authenticity of the originals of such copies, and the accuracy and completeness of the corporate records made available to us by the Company. In making our examination of any documents, we have assumed that all parties, other than the Company, had the corporate power and authority to enter into and perform all obligations thereunder, and, as to such parties, we have also assumed the due authorization by all requisite action, the due execution and delivery of such documents and the validity and binding effect and enforceability thereof. We have also assumed that the Shares will be issued against receipt of valid consideration under applicable law and that the Registration Statement, as then amended, will have become effective under the Securities Act and such effectiveness shall not have been terminated or rescinded. As to any facts material to the opinions expressed herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials.

www.fkhpartners.com

Origin Bancorp, Inc.

April 12, 2022

Page 2

Based upon and subject to the foregoing, we are of the opinion that the Shares to be issued by the Company, when issued, delivered and paid for as contemplated by the Merger Agreement and the Registration Statement, will be validly issued, fully paid and nonassessable.

This opinion is based on the laws of the State of Louisiana, and we express no opinion on the laws of any other jurisdiction. No opinion may be inferred or implied beyond the matters expressly stated herein. This opinion speaks only as of its date and we undertake no obligation to advise you of any change in any matter set forth in this letter.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to our firm under the caption “Legal Matters” in the Registration Statement. In giving this consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Securities and Exchange Commission.

Very truly yours,

/s/ Fenimore Kay Harrison LLP

FENIMORE KAY HARRISON LLP