Sabbatical in Provence

While the original poster on this thread had some confusion, replies there have some info you'll need; see Anita's post about the long-stay visa: https://community.ricksteves.com/travel-forum/general-europe/long-term-visa-and-or-residency-visa. That visa is not the same as a work permit, which you can't get without an employer to sponsor you (unless you have an EU passport).

Schweif, I have no experience with what you propose (sounds fab) and haven't been to France in ages, but I've read some very enjoyable non-fiction about the expatriate life in France. If you decide to proceed, I'm sure you'll turn up some good possibilities at a library, bookstore, or online book-seller. Peter Mayle wrote several books about Provence. They might be a good start. I believe he discusses the French schools.

What a fabulous opportunity for your children! They'll be bilingual by the time you leave.

We are also from S.F. college teachers, so probably have similar tastes to your own. We rented a gite, (at that time on gitesdefrance.com; don't know if it is still in existence). we had a 2 story house in Isle sur Sorgue, with a fireplace and a view of a 12 century castle, could hear the river nearby. Wife walked to nearby Fountaine du Vaucluse each morning for fresh baguettes while husband slept in. We had a car, drove to many wine towns, two towns with medieval synagogues (when the Pope in Avignon gave protection to Jews) which are maintained by France and open to viewing, to St. Remy in Provence where we saw the running of the sheep through town for the annual transhumance, to Senanque abbey, Aix, and so on. Another year we rented a gite on the Lot River in Gaillic, wine country like Sonoma/Napa but more charming with interesting history and rem ants of the Cathars and Knights Templars, , another year near Brantome (near the Dordogne and the Cro Magnon cave paintings). You get the idea: a week or two in each place with a car to have the time to see incredible places. If not a gite, then go for AirB&B with whom we also have had great luck.
As for Provence; St. Maries de la Mer is incredible at the festival of the Rom's patron Saint, Sara, as well as the wildlife preserve with wild bulls, horses and flying sticks of flamingos. Hated the Riviera itself, but loved the towns up hill. If you like dark fiction, read "Parfum" about Grasse. Lyon has great little "bouchon" restaurants and a nearby (by car) medieval town of Perouges, as well as the extinct volcanos near Clermont Ferrand (where we are going in June and back to incredible Rocamador)
when we were in Burgundy wine tasting we found a few small family owned wineries that had students from UC Davis working there, so you might contact Davis to find out if you can be part of some program they might have in France. And...in our opinion, stay in the Midi and south of France, all the north is dreary and not as charming, despite the canals and story-book towns of Alsace.
Sorry everyone, for going on and on!!

I accompanied a sabbatical leave visitor on a year-long position at a research institute in Marseille. But I was not permitted to work: my permis de séjour stated that I was à la charge of the person I was accompanying. We lived in Cassis and he drove in to work each day, while I focussed on improving my French, my cooking and my sun-tan. When we returned to Australia I was 6 months pregnant, and had been able to benefit from the excellent French ante-natal care.

As I understand it, you will need to obtain a permit/visa for temporary residency and it will not allow you to work. Check the French goveernment site.