One month one town/small city

Antibes (since Aix already covered Provence)

La Rochelle on the west coast gets the most sunshine hours other than the Med coast, supposedly. It has great food markets, a word class aquarium, boat trips to the islands and around the bay plus some historical sites thrown in.

The rail line provides links with cities such as Poitiers and Bordeaux plus some of the quaint towns on the coast such as Rochefort. Paris is 2.5 hours by train.

With your summer timeframe, this is a good moment to visit in the north, while the weather is nice, rather than the south. La Rochelle sounds good.

From the weather standpoint I'd probably not choose southeastern France for a June-July trip, but if you do like the idea of the Riviera, I think Antibes is a good choice. The regional rail line would give you access to a multitude of interesting locations. Antibes and Nice both have good markets. The inland town of Biot is known for glass (and also has the Leger Museum), and Vallauris is the town where Picasso create his ceramic works. In about two hours you could be in Sanremo, Italy. Ventimiglia is a bit closer, just across the Italian border; I think it has a large market, but I don't know anything about its quality.

In Brittany, Rennes might be a good option. Within not too much more than hour (less for some destinations) you could be in St-Malo, Dinard, Dinan, Fougeres, Vitre. Vannes, Nantes, Le Mans or Pontorson (for Mont-St-Michel). There are surely other nice places (especially among the smaller towns) that I'm not familiar with. Brittany rarely suffers from summer heat-waves; it does have its share of overcast or rainy weather. I encountered a rather large market (a weekly one, I think) in that area; I believe it was in Dinan.

I would suggest northern France, ie, Amiens. The time frame you mention is exactly that when I have spent in northern France.

Savoie region ...Annecy, Chamonix, Colmar, etc ... perhaps (depending on Covid regulations) could cross into Francophone Switzerland

It’s always possible you have to deal with hot weather that time of the year, so to my opinion it's best to look for a place not too far from the sea.

I have good memories about La Baule-Escoublac an old fashioned beach resort in the vincinity of the Loire estuary west of Saint-Nazaire. Stayed there long ago in July, weather was very pleasant as wel as the atmosphere, ideal for relaxing. Along the boulevard architecture is modern, but there is enough from the pre-war period too. We had our own car, but there is a train station for taking the train to Nantes, Angers, Vannes or Rennes. La Baule is a bit remote so it will take some two and a half hour to reach Vannes, but Nantes needs just one hour. Leaving it for a few days to explore the Loire region is possible too.

Le Croisic west of La Baule is famous for seafood restaurants and also to reach by train. La Guérande is small but nice still having it’s medieval walls, think only to reach by bus. The huge marshlands of Brière just north of it is good for outdoor activities if that is of interest.

I like the idea of spending time in the riviera, but I would choose Villefranche-sur-Mer as my home base. Easyjet and ITA Airways offer nonstop flights from Rome FCO to Nice-Ville NCE for less than $50. I’m sure there are strict luggage restrictions so consider packing light and souvenir shopping at the end of your trip.
Day trips from Villefranche-sur-Mer by train / bus include:
Nice (15-minutes) train
Monaco (30-minutes) train
Saint-Jean-Cap-Ferrat (30-minutes) bus
Eze (15-minutes) train
Vence (2h) combination of train / bus
Saint-Paul-de-Vence (2h) combo of train / bus
Antibes (1h) train
Cannes (1h) train
Menton (30-minutes) train

Blois in the Loire Valley.

Thank you for so many quick suggestions! I am off to do some research and welcome any further thoughts!

We're finishing up a month in Tours. I originally chose it for its train connections, but it's turned out to be a very pleasant small city. Nice parks along the Loire and elsewhere, good shopping along Rue Nationale, and cafés for people-watching in the old center around Place Plumerau. Good tram and bus transportation throughout the city including out to a big shopping area north of town (we had an unexpected need for a large sporting goods store). Great market at Les Halles, especially on Saturdays. And the train connections have worked out perfectly: we've been to Angers, Saumur, Poitiers, Orléans, and Amboise as day trips and took overnight excursions to La Rochelle & Paris. People have also been lovely and helpful even with my less than stellar French.

I spent most of a year in Montpellier and loved it. It is one of the biggest cities in France, but not really a big tourist destination so it feels more authentic. It's just a few miles from the Med so you can take a bus to the beach, has a cute and extremely walkable historic center, and its a university town so lots of inexpensive food options. The train would give you easy access to places like Nimes, Arles, and even Barcelona in a few hours.

I’m actually appreciating the places mentioned all over! I’m still in the early stages and am considering France or Italy. I know it’s smarter to go north for the weather and y’all have given me a lot to look at. Keep it coming!