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This is a campsite we have been to quite a few times:
https://www.camping-montets.com/galeries-photos-chalet
It's simple and not too big - no pool or other "entertainments", up the valley from Chamonix. We'd like to go somewhere else for a change - maybe in Provence or somewhere else in the general vicinity. Any ideas? (I know that this type of question gets asked a lot, but mostly people are looking for a place to amuse kids.)
Choose the area you wish to visit then have a look on Archie's camping.
You can download the poi's to look at in Google earth too
How simple do you want? Quite a few years ago I stayed the night at a campsite around Dijon and the toilets were a hole in the ground with showers only with cold water and basically outside with a tin privacy wall. I think it cost about 2 Euros each for a night.
Most Camping Municipale are simple, good and cheap.
‘Cool Camping’ is useful to see if a campsite allows fires/ dogs/ whatever.
Dutch campsites will give you tent envy.
(Top tip if you like sitting beside a fire on an evening in a campsite that only allows bbq’s: line your off-ground BBQ with foil to make a fire bowl. The reflective surfaces give you a good fire effect whilst only using a few twigs to keep it going. Easily smothered with another piece of foil.)
One of our favourites
https://www.camping-florac.com/
and this thread goes with the recommendation
https://singletrackmag.com/forum/topic/route-guideride-report-france-tarn-cevennes-big-post-pic-heavy/
This is anoter site nearby, even more simple.
http://www.camping-la-tiere.fr/
I've used the municipal campsites when cycling though France. They always seemed to be basic, clean and cheap, and most reasonable size towns have one.
Have a look at campsites in the Ardeche. One of my favourites is at Mazet Plage but I think it might not be simple enough for you. Lots of options though and a beautiful part of France.
Camping le Cezanne near the village of Puyloubier in Bouche du Rhone.
Pretty basic but in a lovely area.
Stoner suggestion is good, the area is a cracker for families and some good riding around, but this campsite is better, quieter and simpler http://www.camping-chantemerle.com/en/
Whatever municipal campsite is near where you want to be. They are all mostly fine. The one in Bonnieux was particularly good, but that was some time ago. Hilltop town and near Buoux if you climb.
We are heading to france for the summern a family roadtrip and have found coolcamping quite a good reference to look for different places. We are staying at the two below which may tick some of your boxes.
https://www.domaine-de-pradines.com/uk/
https://www.greatlittlecampsites.co.uk/ my folks use this to find great small campsites in france
Thanks for all the replies. We booked somewhere from the CoolCamping website. Looking forward to some peace and quiet in the sun!!
Wild Swimming book gets you to great places in the mountains for family swims mountain biking and nice campsites.
We are going back to Camping Lac De Narlay in the Jura. It is simple and beautiful with great lake swimming and some good biking too. Oh and they make cheese, Comté cheese is the big deal along with some of the best wine in France.

Tomaso, it’s really nice around there isn’t it? We have friends who live in Mt Sur Rolle down near Lake Geneva and go skiing sometimes at La Dole. Mmmm Comte.
If you are looking for somewhere to chill and relax we run www.bellessise.com in NE Dordogne which is a small campsite with only 3 pitches in 29 hectares, a natural site, quiet and peaceful. We also have 2 handbuilt wooden cabins. Convenient stopping off site en route to the Pyrenees or Spain. Good local off road and very quiet road riding. Or you can crawl out of your tent and a have a quick 2km blast around Bellessise, before coffee and croissants. We're located alongside the route Dans La Roue de Lawrence D'Arabie "In the wheels of Lawrence of Arabia." In 1908 Lawrence of Arabia made a cycle tour of this region of France following partly the route of Richard the Lionheart.