Unless there is a 'NO'-sign at the beginning of a track, you are allowed to drive any offroad track in France.
Please keep in mind local rules like not going into a forrest when it is a really dry season, etc. Thread lightly and give way to pedestrians, bikes, etc.
The French are very forthcoming when it comes to freedom of movement.
PS: Avoid military terrains. There is no such thing as slightly being allowed to use them. Nothing like the Salisbury Plain! but then France is somewhat bigger, and there are plenty of offroad tracks. I believe that one of the French magazines actually publishes a free roadbook every month. I'll check which one. You can also back-order these roadbooks... after which you can drive the country virtually offroad (Or at least 75% of it!)