Hi, and welcome to the forum.

You'll be happy to know that you are not the first expat to run into this situation and there is even a special license plate for you! You may be able to buy a used car without having to pay the VAT. You get a special license plate that is only valid during the period you will be in the country. At the end of that time, you sell the car back to the dealer and he resells the car.

Cars are more closely controlled on resale in France than in the US, so you should be just fine buying a used car from a car dealer. Even if you bought from an individual, the car has to be inspected before the transfer. (And again on the resale.) If you go through a dealer they will take care of all that stuff.
Cheers,
Bev