Great art work not in Paris

We enjoyed the museum in Orleans. Not too large and very nicely organized. Orleans is a wonderful place to spend a few days too.

I really enjoyed The Musée des Beaux-Arts de Rouen and Rouen in general.
When I visited last September I had the room with the Monets all to my self for about an hour - heaven.

You could check this website for some ideas. Just skip the initial ones listed that are in Paris. Nice, and the area around the French Riviera, has several good art museums.

I agree with checking out the various museums in Nice, but also in the surrounding Riviera towns, Antibes, St. Paul de Vence, etc. Also search this forum for commentary on the several art museums in Lyon. Both Nice and the Lyon area offer plenty of good food and other interesting sightseeing when your eyes get tired.

For some reason, the collection at the Chateau de Chantilly, short distance from Paris, is not know to many travelers. From their website: "The second largest collection of antique paintings in France after the Louvre." Other sites/sights in the town as well.

https://chateaudechantilly.fr/en/chateau/the-art-galleries/

The archeological museum in Arles has a terrific collection of Roman mosaics and sculptures. There's also the Gallo-Roman Museum in Lyon.

For medieval, consider the Museum Œuvre Notre-Dame in Strasbourg. I'd also give a very enthusiastic thumbs up to the Museum of La Cour d'Or in Metz for their medieval collections (as well as 16th - 20th centuries, though not as strong)

Musée des Arts décoratifs et du Design in Bordeaux is especially good for 17th and 18th century furniture, glass, porcelain, etc.

The Musée de la Faïence in Sarreguemines is a dedicated to French ceramic art, especially from the art nouveau.

Bordeaux also has the CAPC Musée d'art Contemporain de Bordeaux for contemporary art.

The Bastion—Jean Cocteau Museum in Menton.

The Rosary Chapel or Matisse Chapel in Vence.

And finally, I'll give an honorary nod to the Institut Lumière as a museum dedicated to the art and history of cinema. It is in Lyon.

Lille has a terrific lineup of art museums spanning many eras: Beaux-Arts Museum, La Piscine, Musée d'art Moderne (LAM), Tripostal, and possibly others! Also Louvre Lens is close by.

And one of the favorite museums I've had a chance to visit in the country is the Grenoble museum. The collection packs an unexpected punch, and is a definite highlight of any visit to the city, which is otherwise only moderately interesting.

The Unterlinden Museum in Colmar is quite good. I'm sure there are worthwhile museums in Strasbourg as well, but I haven't been there recently.

I agree about Nice (at least six art museums) and smaller towns along the Riviera and up in the hills--lots of good options there.

It seems to me that France is unusually rich in art museums outside its capital city. There just always seems to be something, no matter where you are--so much so that I'm struggling to think of specific places.

Nancy and Limoges are both good for decorative art. Biarritz (otherwise far from my favorite place) has a good Asian art museum--primarily decorative art from South Asia, as I recall.

If you Google "art museums Nice" or simply "museums Nice", the resulting links will cover nearly all the local options of significance. "Gallery" is a riskier term to use, because that will also find commercial art galleries, which may not be what you're looking for.

Lyon has beautiful museums and is one of my favorite cities outside of Paris, easy to reach by speed train in a couple of hours

As mentioned by @Balso visit the Louvre in Lens! Can be combined with Lille.