My advice would be to squeeze in Normandy if you can especially over Loire valley but I really like WWII history. Mont St Michel is that direction and it is also spectacular, especially at night. Normandy is a longer trip than Loire so may not be able to make it work but I would try.

Villefranche is a great place to stay on the Riviera. Monaco isn't really worth it unless you want to cross another country off the list or see exotic cars. Better to go to Antibes or Eze. Be sure to spend time in the old part of Nice and walking on the Promenade des Anglais. There are some great restaurants on the beach there. I have a friend who is from Nice and his favorite place to eat in Nice is Le Galet. Make a reservation to eat there around sunset, it's gorgeous.

Chamonix blew me away when I went. The scenery was amazing. The tram to Aiguille du Midi was impressive. The Mer de Glace and the tram to Hellbrenner's pass into Italy were both closed when I was there but I would've loved to have done both of those as well. There is a fun old part of town to walk around and find places to eat.

Really jealous of your trip, it sounds amazing.