Just got back from Alsace, lovely region, briefly visited Germany (black forest) as well while we were there. Lots to do, lots to see, beautiful little towns, great wine. Have also had fantastic holidays around Dordogne which would be fun with teens, especially if they're active types, canoeing is great and cycling (although hilly!)
We've never had a bad holiday in France. We've been to the Charente Maritime and love La Rochelle and Ile de Re. We had a superb holiday in the Lot/Dordogne region near Sarlat. This year, we are driving there for the first time and venturing into the Loire Valley. We have primary age DC and we've always stayed in a gite that shares communal facilities like a pool with a handful of other gites so that the kids can make friends and you can have the chance to socialise with other adults.
All of France is interesting, has history and things to see. Literally, you could go anywhere and find lovely little towns with castles, old houses, a museum, etc. The entire country is a treasure trove.
Here is an article comparing Gascony with the Dordogne (both very popular areas with British tourists). It might give you some idea of what is on offer. It's a lovely area, btw. You could do a lot worse than go there for your first taste of France.