Hi @Corona , just in case you are still not square on requirements for taking your cat to France, this website gives all the details very clearly
Step 1 in UK - Visit the vet.
You will need to visit the vet to obtain an animal health certificate. Your pet will also need a microchip and rabies vaccination.
Before booking an appointment, make sure that your chosen vet is an ‘official veterinarian’ (OV). Not all of them are. Only OV’s will be able to issue an animal health certificate for your pet.
At your appointment, your vet will administer your dog, cat or ferret with a microchip and rabies vaccination, if your pet hasn’t already had them. They will also perform a basic health examination to ensure your pet is healthy enough to travel. Once the veterinarian is satisfied that your pet is ready for travel, they will review all the paperwork and complete your pet’s animal health certificate.
NB
Plan early!
The animal health certificate will confirm a still valid rabies vaccination given earlier. If the animal has had no previous rabies vaccination the vet will administer a primary one. **You then wait 21 days for the vet to do the antibody test before issuing the certificate. Occasionally, the rabies vaccine must be redone because the first one failed to produce antibodies. So, another 21 day wait is needed.
Step 2 in France Visit the vet
Once in your destination EU country, your pet can visit the vet there to obtain their EU Pet Passport. These can no longer be issued in the UK due to Brexit.
Since you are planning to voyage your kitty back and forth to France (or Europe) with you, it is best to get an EU passport while you are in France. Apart from making entry/exit smoother it is handy for keeping vaccine records and microchip details.
NB. France rabies vaccine is annual. For the vaccine to be valid in an EU pet passport it must be given and signed by the vet in France. A UK vet cannot enter into an EU passport.
This is unfortunate because the UK vaccine covers 2 years but that’s not a great compensation for having to pay the UK vet for an animal health certificate each and every trip to France if your pet doesn’t have an EU pet passport.
The UK recognises a valid EU pet passport with microchip and current rabies vaccination (done in France) upon re-entry.