There are many very nice B-roads (départementale here

when you have time. Depending of where you arrive in France, if it's Le Havre or Dieppe you can go to Le Mans but perhaps you already know. There is the museum to visit. Going south in diagonal, further south there are very nice roads in the Creuse department, going to Gueret or Aubusson for exemple (between Limoges and Montluçon). If you have time to do some more miles and go to Lyon (nice town) I can recomand a very nice Automobile Museum, the Musée Henri Malartre in La Rochetaillée a few kilometers North of Lyon along the Saone river(only about 10/15 I think. The museum is in a castle with a very beautiful scene and very old cars, bikes and motorbikes.
If you are not going to Lyon, in the Massif central there are many very nice twisting roads and then in the Haute Loire department going to Le Puy (very nice view and beautiful landscape in he area including the Le Puy town)and then in the Ardèche department going towards Aubenas and Vals les Bains. Then you can rejoin Avignon (nice to visit also, don't go too far on the bridge...

)A few kilmometers south there is a nice little auto museum at Orgon (near Cavaillon) along the "Nationale 7" road. In this area some very nice villages and landscape are worth to be visited (on the other side of the A6 motorway) : Fontaine du Vaucluse, L'Isle sur la Sorgues, les Baux de Provence...
This is just one way but there are many others as nice possible!
A few years ago I made a trip during my holidays from Paris to Marseille nearly all the way by B-roads. I had some wonderful drives

with the Elise especially in the Saône et Loire, Haute Loire , Ardèche departments , on twisty and empty départementales, a great joy with fine weather and beautiful landscape. Hopefully my girlfriend likes the car and enjoyed also the trip, some times quite fast in the corners.