If it's "days coming up" fairly soon, the overall tendency is toward hot, so maybe avoiding the south (your last trip in Sarlat-le-Canada) would be good, and maybe getting somewhere near some higher-altitude roads might provide some cooler options on hot days (esp if get most of the climbing done early in the morning, save most of the downhill for the afternoon).
One area that's near higher mountains and with lots of pretty valley roads is in Savoie between Chambery + Albertville. The area has pretty farms, some with horses + cows, vineyards, two giant lakes, and dramatic rock walls + peaks rising above the wide valley. Lots of train service between Paris + Chambery (some people who love the mountains there do weekly commutes back + forth to Paris).
From somewhere in the valley between Chambery + Albertville, you could do various day trips:
(a) valley ride thru Chambery to (and around?) the Lac du Bourget and back;
(b) valley ride past Albertville and Faverges to Lac d'Annecy and ancient city of Annecy, ride back around other side of lake and different sides of valleys;
(c) south toward Grenoble: like south in the foothills and return north in the valley (or in the foothills on the opposite side).
various mountain rides in the lower mountain groups just next to the valleys, or for a couple of days take a bus/train to place up near the famous high passes. Or there's a famous mountain pass right there, Col de la Madeleine, which could be included in a loop around its W side with some valley riding.
There's bike routes on the web, and some routes in that area with signs on along the roads (also a recent English-language guidebook for road-cycling).Some might suggest basing a little further north like around Annecy in Haute Savoie -- but there I think you'd have fewer options for less-hilly rides.
Lots more interesting farm country between there and Lyon -- and higher (less hot?) around the Massif Centrale (also with some road-signed routes).
If you knew how to carry your bike on trains (I don't), might even be able to just stay in Paris, take the train out each day to a different route in the surrounding countryside.
And if you don't care about heat or altitude or north-south . . .
France is a big place.