In 10 days you could do both, but -- as you noted -- it is a very long drive from Mont St-Michel to Orange, and then you have to get to & from Paris, assuming you're flying in & out of Paris. As earlier comment suggests, you might want to take the train.
If you drive, be aware that navigating on French highways involves knowing the major cities where the route points you -- even if you aren't going to those cities. For example, on the A28 near Le Mans, northbound is "direction Rouen" and southbound is "direction Bordeaux." It's kind of like the Metro in Paris.
I think the logical route would take you via Rennes, Le Mans, Tours, Bourges, Vichy, Lyon, and Valence. Outside of Tours the A85 takes you quite near the famed Chateau of Chenonceaux, so you might consider breaking up the trip with a stop in that area. Perhaps overnight, allow time to tour the chateau, and then continue to Orange next day.
Do you want to spend any days in Paris?