As of 14 March 2022, the Government of France no longer requires citizens or visitors to produce a Vaccine Pass (Pass Vaccinal) to go almost anywhere in the country.
However, face masks must still be worn while on public transit.
Recently, prior to 14 March, persons wanting to enter restaurants, bars, museums, movie theaters, etc., were required to show a government-issued Pass Vaccinal as proof of vaccination against COVID-19.
Now the one remaining exception to the relaxed COVID-19 rules is that a Pass Sanitaire must be shown to enter medical facilities, such as clinics, hospitals or nursing homes. To obtain a Pass Sanitaire, one must (1) be fully vaccinated, or (2) present a negative result of a PCR or antigen test taken within 72 hours, or (3) present a certificate of recovery. Go here for more information from the French government.
And remember that to enter France at all, unvaccinated travelers age 12 and up must present a negative PCR test result taken within 72 hours, or a rapid test taken within 48 hours of entering France. Also that what constitutes "full vaccination" varies among vaccines. Seek reliable, up-to-the minute advice before traveling.