Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

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We consent to the incorporation by reference in the Registration Statement of Peoples Financial Corporation on Form S-8 (No 333-144181) of our report dated March 18, 2026, on our audits of the financial statements as of December 31, 2025, 2024, and 2023, and for each of the years then ended, which report is included in this Annual Report on Form 10-K to be filed on or about March 18, 2026.

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/s/ EisnerAmper LLP

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EISNERAMPER LLP

Baton Rouge, Louisiana

March 18, 2026