Trips to Switzerland, Bavaria, and Austria have all been by train, bus, and/or bicycle. Driving trips in France have been in Provence and Dordogne in the south, Lyon and some of the mountains to the west, Normandy in the north, and Brittany way, way west, and Bordeaux wine country in the southwest. France is big—are you going to interested in one particular section, or many. As noted above, big cities generally work better with your car parked the whole time, or you rent your car as you leave, and maybe turn it back in at the next big city.
Provence is great for a driving vacation. Maybe base yourself in San Remy, if you want to stay in one spot and drive to places for a day. Lots of tailgaters, though, fewer in other parts of France.
Or do you want to tour in a loop, staying 1 or 2 nights, before moving on? Could start in Provence, head north to Lyon, cut east to Switzerland, Germany, and Austria.
Or start in Bavaria, rent your car there, head from there to France, then Austria, then circle back thru Switzerland to Bavaria, where you can turn in the car?
Other parts of France are excellent for drive touring, but farther from those other countries than Provence.