MSM and Loire advice needed

Though I did not stay on the Mont (wish I could have), I think only 1 night is sufficient. As far as the Loire valley, I would suggest staying in either Chinon or Amboise - both much smaller a calmer than Tours.

From CDG, take the train to Tours and rent a car there. Use it to tour the chateaux, drive to MSM and then to either your hotel or to CDG. If your flight is early in the day, return your car the night before and take a cab or shuttle bus to your hotel. With only 6 days on the ground, make the most of your precious time.

This is a short trip from the USA. There's a Bookmark problem for regular posters right now, but your question has been very frequently discussed, and you can get a lot of input from the Search box top center. One example:

https://community.ricksteves.com/travel-forum/france/travel-to-mount-st-michel

I'm one of those who doubts the need to sleep on MSM, and even some who consider it essential admit that the accommodations leave something to be desired.

EDIT: Second link added:
https://community.ricksteves.com/travel-forum/france/normandy-brittany-thoughts

I'd suggest not driving on your arrival day because you'll be tired and jet lagged. A TGV from CDG to St-Pierre-des-Corps, close to Tours, takes a little over two hours. Then you can take a local train five minutes into Tours, or rent the car at St-Pierre, depending on whether you'll be spending significant time in Tours itself and what the parking situation will be at your hotel. Tours is a big enough city that you might do better basing in a smaller town for chateau-touring, if your points allow that.

I haven't stayed overnight at MSM, but I would have if I could have. One night should be enough as long as you have some time the day before or after to explore the island. You'll need at least four hours to drive there from Tours, and five or six hours from MSM to CDG. The fastest route takes you close to Honfleur and Rouen, either of which would be a nice stop if time allows.

It's a short timeframe but a good plan to use that time well.

If you'd rather stay in a place less congested than Tours and not as far out as Chinon, I recommend Azay-le-Rideau. We stayed in the Hotel Biencourt and loved it, would stay there again any time. Delicious breakfast buffet, charming property, very helpful hosts. From there the drive to Chinon is a straight shot and takes about half an hour. You are also in easy driving range of Villandry. It's a longer drive (about an hour) to Chenonceaux, still doable in a day.

I am assuming we should plan to try to stay at a hotel on MSM for the best experience.

Opinions vary. We stayed at a hotel just across the bridge from MSM and thought that was better than staying on MSM. MSM lit up at night is beautiful, as is seeing it during the day. There are frequent free buses across the bridge until midnight. One advantage of staying across the bridge is that you can park at your hotel; when staying on MSM you park at the more distant day lot and take a bus with your luggage.

I think one night is enough. Do what RS says and arrive later in the afternoon, although that late in the year you should check when sunset is. In the afternoon as the daytrippers leave it is less crowded. After dinner go back for the night view, the next morning you have time for another visit before the buses arrive en masse.

As a side note, restaurants serve dinner and close earlier at MSM than in larger cities in France. So be sure to check the hours at the restaurant you are considering.

I don't think you need more than one night on MSM, but I highly recommend you stay on the Mont itself. The days are extremely crowded with bus loads of tourists, and there is nothing like taking a magical walk late in the evening and/or early in the morning when you have the little lanes and views to yourself. Don't let anyone talk you out of it and you won't be disappointed.

We drove our rental car from Mont St Michel to the Loire Valley. It made for a hilarious situation at a toll booth.

I cannot imagine the Loire without a personal car.

Staying at the Mont is a personal choice. Don't forget to factor in your exit strategy in the morning and how it affects the day's journey.

One night visiting MSM is good unless you want to base there to visit other nearby places. Several years ago we stayed 2 nights on the mainland (at Les Valtieres du Mont Saint Michel - great view of MSM!) and did a day trip to Cancale. What I would do is rent a car at CDG and drive to Tours after landing for your time in the Loire. Then go to MSM and then back toward the airport for your last night. Suggest looking for a hotel in a quaint little town on the outskirts of Paris within an hour's drive of CDG unless you have an early morning departure - then stay by the airport.

Opinions vary, but renting a car at CDG after max 3-4 hours of sleep on the flight from the East coast, to navigate all around the heavy-traffic Paris region and drive to Tours does not feel like the best option. The drive takes 3 hours in perfect traffic, more likely 4 on a weekday morning.
The current schedule has a train from CDG to Tours St Pierre des Corps at 11.16 am, arriving at 1.05 pm: you can then rent a car there.

Likewise on the way back, the drive from MSM to Paris is very, very boring. I would drive to Rennes instead, drop the car there, and take the train to Paris: 90 minutes instead of 4 hours! Car rental drop off at Rennes station is a bit annoying (you have to drive to the 10th floor of a parking garage...), but still nicer than the A11 to Paris.