Two weeks in Burgundy and Provence May 2018 ?

Since you're coming from Mulhouse you might want to stop by Baumes-les-Messieurs. It's a scenic little town in a steep-sided valley (I believe it's a glacial cirque) cut into the Jura Plateau. It's a little out of the way from the direct route Mulhouse-->Dijon-->Baune--->Lyon, but worth the stop if you have the time. There's a beautiful waterfall just south of there (Cascade des Tufs).

South of Mâcon (between Beaune and Lyon) is la Roche de Solutré. This is a limestone scarp you can hike up nestled in a pretty valley of vineyards. The Pouilly-Fuissé wine is from that area. There's a small natural history museum at the base of the rock with a good collection of stone-age tools found in the vicinity of the rock, which apparently was a destination for paleolithic hunters in the area. There once was a hypothesis that hunters would flush herds of prey up the rock and over its cliffs to kill them for food, hides, and bones because of the large amount of animal bones and stone tools found around the rock, but now it is believed that the rock had some distinctive meaning in that culture and was a draw by itself, not for any hunting purpose. I found it interesting how similar the tools these guys used many tens of thousands of years ago are to those used by the native people of North America.

In and around Lyon, a few things to have on your list of possibilities:

• A nice walk to get a sense of the central part of town is to head north from Place Carnot near the Perrache train station on the pedestrian way rue Victor Hugo, through the huge Place Bellecour, past the Place des Jacobins with its beautiful white fountain, and on to the Place des Terraux. A few architectural things to check out on your route are the Chamber of Commerce (former bourse) near Place des Cordeliers, the current (?) bourse at Palais du Commerce, and the Opera house across from Hotel de Ville. You go from gritty (near Perrache) to glitzy (the shopping areas along rue de la République on the way to Place des Terraux. The city of Lyon is finishing the reinstallation of the Bartholdi fountain (same guy that did the Statue of Liberty) in Place des Terraux, and it looks as good as new. After the long walk, I like to buy a cold drink from a local shop and go through the exterior entrance of the Musée des Beaux-Arts, which also is located at Place des Terraux. Inside is a peaceful, leafy courtyard one can visit without paying admission to the museum where you can sit on a bench in the shade and enjoy the quiet.

• If you like to visit churches, the Basilica Notre Dame de Fourvière near the end of the funicular leaving from the medieval old town area is one of the most highly decorated churches I've seen (mostly mosaics). There are some Roman ruins near there as well, a good Gallo-Roman museum, as well as a viewpoint overlooking the city. When showing visitors Lyon I like to walk down from Fourvière through the forested Parc des Hauteurs. While on the quiet, leafy paths heading downhill, it's hard to imagine you're in the second largest metropolitan area in France.

• Les Halles Paul Bocuse, named after the recently-deceased chef, is a pretty amazing food market for a walk-through with plenty of places to stop for lunch.

• I would also recommend making your way over to Parc de la Tête d'Or, renting a bike (they're cheap) and riding a circuit around the park. It's got several beautiful gardens, sculptures, trees, a free zoo, Victorian-era greenhouses with different climactic zones maintained along with different ecologies, a lake with an island containing a massive memorial to WWI (and other conflicts), as well as a buvette (a small restaurant) where you can have a glass of wine and watch the ducks and geese under the shade of lakeside trees.

There's a lot more, but I've probably bored you enough and am nearing the maximum length for a comment.

Besides Baumes-les-Messieurs, which is definitely worth seeing, there are several other cities and towns in that part of the Jura that are worth a stop, including Besancon, Dole, and Arbois. My blog post from our 2010 trip has some photos from Dole and Baumes:
http://mainelywinenews.blogspot.com/2010/04/back-in-usa-jura-recap.html

Some highlights for me in Burgundy:

The Abbey at Fontenay, Beaune, bicycling through countryside and vinyards, Vezeley, small towns of the Serien valley. The tasting lunch in Aloxe-Corton.

In Lyon: Food throughout; don't miss the greenmarkets. The Roman theater and odeons and the Gall-Roman museum. Walking tour of traboules in old town. Toodling about on Lyon'd bike-share system. The funicular. The sobering Resistance museum, housed in former Gestapo HQ.

Provence: Roman antiquities in Arles, Orange, and NImes, including the must-not-miss Pont du Gard. Market day in Arles. Boulliabais on the quay in Marseille. (reservations required). Walking trails in the Luberon.

Merci !!! Adding these to my possibilities list! We're excited to see a new-to-us area of France.