Looking for two cities to base ourselves outside Paris

I did something similar last fall. These aren't the easiest areas to tour without a car. I have traveled to this area in the past with a rental, but for various reasons, didn't want to solo drive on my last trip.

In the general area of MSM, I stayed in Bayeux. I used Overlord tours for a DD beach tour, but they also have tours to MSM (other companies from Bayeux do also, but I can personally recommend Overlord). Train connections in that area to small towns aren't great. Nearest train to MSM is Ponterson. https://www.abbaye-mont-saint-michel.fr/en/visit/practical-information

In the Loire, I used Amboise as a hub. Three castles walkable from city center and a historic center to explore. By train, I explored Tours, Chambord, Chenonceaux , and Blois. There are also day tours from Tours to various castles - that would have been easier than self-tour by train, but as a solo traveler, the tours I wanted didn't run for lack of numbers (2 minimum required.) Acco Dispo is the company I tried - they were great in trying to help me and I will book with them when I return with a companion next summer.

I'm not a big drinker myself, not interested in vineyards. This didn't impact my visit.

I do enjoy the differences in the chateaux - all are unique and I enjoy the individual histories, architecture, etc. If you think that chateau after chateau might be too much, you would not be alone. Many visit one or two of the larger chateaux and stop there.

In addition or an alternative to Versailles, you might find the relatively easy access from Paris to Fontainebleu or Chantilly as preferable to the Loire by public transport. (Train access, even where possible in the Loire, doesn't have ideal arrival and departure times in my experience.)
https://www.chateaudefontainebleau.fr/en/
https://chateaudechantilly.fr/en/

This is one of my all time favorites doable from Paris, but may require a taxi ride from the station whereas the above are walkable from the train stations.
https://vaux-le-vicomte.com/en/

I suggest taking a look in detail at the train connections that are possible to see if the areas you have targeted will have the access you would like. Several possible search sites, here's one:
https://www.sncf-connect.com/app/en-en/home/search/od

Strasbourg or Colmar. It’s about a 2 hours train ride and a completely different vibe. Prepare to fall in love. We spent 4 nights in July and loved it so much we returned for 4 nights during the Christmas markets. Tons of adorable towns to explore.

IMO 7 days in the Loire is too long. travel4fun's suggestion of Colmar/Strasbourg is a good one. So, 7 days outside of Paris.(7 nights?)
If seven nights, train to Normandy for MSM. Pick your location of where to stay. Figure two nights involved with this, and 2 nights (1 1/2 days after arrival) in the Loire (Amboise?). Then back to Paris, change train stations and off the Strasbourg or Colmar for 3 nights. TGV between Paris and Strasbourg takes a little less than 2 hours.
(Even if you don't drink wine, and even if you still go to Versailles, seeing Chenonceau and 1 or 2 other chateaux in the Loire is worth doing. The Loire and Cher rivers area is lovely.) Have fun on your trip!

Thanks for all of your thoughtful replies. I would consider driving to Mont Saint Michelle, St Malo, and Dinan if the coast is truly worth seeing and there isn't "big city" traffic and roundabouts (my palms are sweating already).

This is the area where I have driven in past years. I don't recall it being particularly stressful. Much is rural and smaller roadways.

Roundabouts - when in doubt, circle again until certain of your exit. That's my long-tested approach - but the current GPS options are so good with saying "take the 2nd exit" or whatever that roundabouts don't bother me anymore. You will encounter some.

Look into Caen for a rental. There are some agencies near the train station.

Some discussion here that might be of interest if you haven't seen it:

https://community.ricksteves.com/travel-forum/france/help-tweak-my-normandy-itinerary-please