Quoting the UK Gov website https://www.gov.uk/foreign-travel-advice/france/entry-requirements
Travellers who are fully vaccinated do not need an essential reason to travel to France and do not need to self-isolate on arrival. Fully vaccinated travellers will need to present the following documents:
... evidence of a negative PCR test result taken within 72 hours of departure, or a negative antigen test result taken within 48 hours of departure
a completed ‘sworn statement’ .... This can be found on the French government’s website
proof of vaccination status
Vaccination status
...“Fully vaccinated” is defined by the completion of a vaccination schedule, specifically:
2 weeks after the second dose of Pfizer, Moderna, Oxford/AstraZeneca
4 weeks after the single and only dose of Johnson & Johnson
2 weeks after the single dose of any of the above vaccines if you have previously tested positive for COVID-19