I think you will eventually need a french car there is some rule about only using a right had drive for a certain period
This isn't correct. We lived there for 11 years and I only ever drove RH drive cars.
As @AnnaDelvorkina says, you do need to register your car in France, get French plates, French insurance and have a CT (controle technique - equivalent to MOT). French CTs are valid for 2 years.
It is a very straightforward process and there are lots of online groups which can help.
Cars (even second hand) in France are £££££££££s.
The main thing to be concerned about is your licence. If your photocard expires and you are living in France you cannot renew it using a UK address - plenty of people still do, but it isn't legal to do so (same with insurance/MOTs!).
There was a mad rush a few years ago to get people to switch to a French licence. It was a nightmare with systems crashing, departments being overwhelmed and people left without any form of licence - not sure what the situation is these days. I used to belong to a FB group run by Kim Cranstoun, not sure if that is still running as it is no longer relevant to me, but worth having a look.