My feeling about must-see places is that there are either none (every traveler's interests are different) or too many (in most European countries it's hard to travel 10 miles without coming to an interesting stop). Gooster has mentioned quite a few places that I found worthwhile.
I totally agree about the need for variety--except when it comes to picturesque towns (or historic districts of larger places). I just can't get enough of those.
Between Sarlat and Carcassonne, your route takes you past Toulouse, which is a very handsome red-brick city. It has a look very different from the other places you'll see. It's large, though, and I'm not sure how you would deal with a rental car there; you might need to park it quite some distance from the beautiful historic district.
Between Carcassonne and your port for Corsica (Marseille?) you have Narbonne (good-sized) and Montpellier (large university town with atmospheric historic district). Not far off your route is Pezenas, which I learned about on this forum; it's a cute town know for crafts. There's also Sete, a coastal town that I enjoyed, though I preferred Pezenas. The marshy Camargue area is just south of Arles. Aix-en-Provence is an attractive city in its own right, but it also has a very interesting WW II site, Camp des Milles, a transit and internment camp blessed with very comprehensive English-language explanatory material.
If I were choosing between Dijon and Reims (both not quite on the direct route, I think), it would be Dijon all the way. Reims is just not as physically attractive as Dijon. However, there's the champagne thing going on in Reims. I think I remember recommendations for Sens but don't know anything about it. Troyes I really liked. It has lots of half-timbered buildings; gets lots of European tourists (perhaps primarily French), but very few Americans, and I never saw a tour bus. Right near the highway is Beaune, known for the Hospices de Beaune (aka Hôtel-Dieu).