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France has a lot of good places in natural parks away from cities. In pic related, places in red have particular rules (no camp fire, no tents, etc...). I recommend south or east of france for better weather conditions, the north-west is pretty rainy.
According to what I know it's ok to place your tent freely as long as you don't stay for too long. Camp fires are forbidden in summer and you must be 200m away from a forest if you want to make one. Vehicles are often forbidden. Trapping animals is forbidden too, but I guess it's ok to trap a rabbit if nobody sees you.