As French nobleman and military leader Monsieur de La Palice might have said, leaving whenever you like means being completely free to choose when to go. So it's no longer a question of high season or low season, but just as the fancy takes you.
Freedom to choose where to go
Choosing a campsite which is open all year round, wherever it is located, means you can break free from the season's "Great migrations" and explore a region, a city or a popular tourist attraction anywhere in France. It also means you can get reasonably priced accommodation during your break or at the very least for a far better price than by using traditional "permanent" hotels.
Let's take Paris as an example. Instead of looking for hotels or rentals which are exorbitant for the closest ones and relatively far away for the more affordable ones, why not try the campsite? There is a campsite in the heart of the Bois de Boulogne right in the middle of the 16th arrondissement in Paris - the Camping de Paris Bois de Boulogne (Huttopia). This four star campsite, and all the services that go with it, can serve as a 'base camp' for exploring the capital. A shuttle drops you off at the Porte Maillot station, from where you can get the bus or the metro to anywhere in the capital. The same goes for Bordeaux with the Village du Lac situated in Bruges, less than half an hour away from the city centre by public transport. Fancy exploring the 'Pink City' of Toulouse and getting lost for a day in the Cité de l’Espace (Space City)? You could stay in a few campsites there as well. It is the same in every region in France, from the Atlantic Coast to Mont Saint Michel and the Côte d’Azur, and in inland France, too, with 2 to 5* campsites of all sizes with every level of service.
Freedom of price
Going on a camping holiday whenever you like also means possibly great prices and, in any case, lower prices than you would get during the low or the high season. The downside is that the level of services offered will not necessarily be the same as in spring and more so in summer. That said, if you have decided to explore Paris, Toulouse, Bordeaux or any other major tourist destination, you don't necessarily need to have a swimming pool or a restaurant...
And to find a campsite which is open all year round in the major regions of France: