Farm Fresh Food for Families Act of 2023 This bill expands the WIC Farmers' Market Nutrition Program (WIC FMNP) to include community supported agriculture (CSA) programs and makes further changes to the program. The program awards grants for states to provide vouchers and coupons that participants in the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) may use to purchase fresh produce at approved venues (e.g., farmers' markets). The bill adds CSA programs to WIC FMNP, which currently may include farmers' markets and roadside stands. (Under a CSA program, farmers grow food for a group of shareholders or subscribers who pledge to buy a portion of the crops grown for that season; a state agency may purchase shares or subscribe to the CSA program on behalf of individual WIC FMNP participants.) The bill also reauthorizes WIC FMNP through FY2029 and increases the federal share of benefits a recipient may receive under the program. Specifically, the bill raises the annual minimum benefit to $20 (currently set at $10) and removes the annual cap on benefits. Further, the bill removes a requirement for states to provide matching funds that are equal to at least 30% of the administrative costs of the program.