LIMITED POWER OF ATTORNEY

       The undersigned, Simeon A. Thibeaux, a principal shareholder of Red River
Bancshares, Inc. (the "Corporation"), hereby authorizes and designates each of
R. Blake Chatelain; Amanda W. Barnett; and Fenimore, Kay, Harrison and Ford,
LLP, as my agent and attorney-in-fact, each with full power of substitution to:

       (1)    prepare and sign on my behalf any Form ID for filing with the
United States Securities and Exchange Commission, generate or update on my
behalf any applicable EDGAR access codes, and request on my behalf any EDGAR
passphrases or other related filings codes, if necessary;

       (2)    prepare and sign on my behalf any Form 3, Form 4 or Form 5 under
Section 16 of the Securities Exchange Act of 1934 or any amendment thereto and
file, or cause to be filed, the same with the United States Securities and
Exchange Commission and, if applicable, each national stock exchange on which
the Corporation's stock is listed;

       (3)    prepare and sign on my behalf any Form 144 Notice under the
Securities Act of 1933, or any amendment thereto, and file, or cause to be
filed, the same with the United States Securities and Exchange Commission;

       (4)    prepare and sign on my behalf any Schedule 13D or Schedule 13G
under the Securities Exchange Act of 1934, or any amendment thereto, and file,
or cause to be filed, the same with the United States Securities and Exchange
Commission and, if applicable, each national stock exchange on which the
Corporation's stock is listed; and

       (5)    take any other action of any type whatsoever in connection with
the foregoing which, in the opinion of such attorney-in-fact, may be of benefit
to, in the best interest of, or legally required by, the undersigned, it being
understood that the documents executed by such attorney-in-fact on my behalf
pursuant to this Limited Power of Attorney shall be in such a form and shall
contain such terms and conditions as such attorney-in-fact may approve in such
attorney-in-fact's discretion.

       The undersigned hereby grants to each such attorney-in-fact full power
and authority to do and perform any and every act and thing whatsoever
requisite, necessary or proper to be done in the exercise of any of the rights
and powers herein granted, as present, with full power of substitution or
revocation, hereby ratifying and confirming all that such attorney-in-fact, or
such attorney-in-fact's substitute or substitutes, shall lawfully do or cause to
be done by virtue of this Limited Power of Attorney and the rights and powers
herein granted.  The undersigned acknowledges that the foregoing attorneys-in-
fact, in serving in such capacity at the request of the undersigned, are not
assuming, nor is the Corporation assuming, any of the undersigned's
responsibilities to comply with Section 16 of the Securities Exchange Act of
1934.

       This Limited Power of Attorney shall remain in full force and effect
until the undersigned is no longer subject to Section 16 of the Securities
Exchange Act of 1934 with respect to the Corporation, unless earlier revoked by
the undersigned in a signed writing delivered to the foregoing attorneys-in-
fact.


                 [Signature Page to Limited Power of Attorney]


       IN WITNESS WHEREOF, the undersigned has caused this Limited Power of
Attorney to be executed on this 22nd day of January, 2019.



                                        /s/ Simeon A. Thibeaux
                                        ---------------------------
                                        Simeon A. Thibeaux



       SUBSCRIBED AND SWORN TO before me this 22nd day of January, 2019.



                                        /s/ Dianna T. Pennington
                                        ----------------------------------
                                        Notary Public

                                          Dianna T. Pennington
                                          Notary Public ID Number 51428
                                          Grant Parish, Louisiana
                                          Commission is for life

My Commission Expires: