We are planning to move to France next year from Poland (temporary residence). Car prices here are as far as I can see cheaper than in France. Does anyone know if the process of reregistering a car in France is difficult (and expensive)?
If you're going solely for the cheapest purchase price for the car, then fine. But implicit in the pricing of cars (new and used) in France are some of the controls you'll need to pay for on the side if you re-register. I think you'll probably still need a controle technique in order to register the car here in France (at least if the car is a used one) - but check this site for details: https://www.service-public.fr/particuliers/vosdroits/F1050
If you buy a car here in France through a dealer, the dealer will handle the various paperwork (and get the controle technique). It's always going to be a bit tricky proving your residence in France when you've just arrived, but the dealers usually know the local prefecture pretty well and can help you through the process.
I think you only need the controle technique if the car is more than 4 years old.
Importing from one EU country to another should be slightly easier than bringing a car in from outside the EU - eg as your original certificate of conformity should be accepted in France. This page https://hubpages.com/travel/destination_france_car_registration seems to explain the process in a bit more detail than some placed I've looked.
We're planning to bring our car from the UK for the same reason - we bought the car much cheaper in the UK than we could have (for the same age & model) in France.