France in June = busy, book early, otherwise a 'flexible' itinerary (booked on the fly) requires a little more broad-mindedness for types of accommodation and facilities available, will also require more language knowledge. Dont try to eat the same things you eat at home, eat & drink what is local to where you are in France and you will usually find the locals are happy to help you experiment within your comfort zone. Just like the food, most wines are sold by the district they are grown in and not so much by grape variety. French folks always have a HUGE pride for their local area.
When touring old battlefields, take a picnic and sit in the area and soak up the atmosphere. Not many of the battlefield memorials are in or near a town.
When visiting Bordeaux, take a side trip to Arcachon & eat some crabs or oysters. And @Willin' suggestion above fits this side trip and is worthwhile - many cultural shifts an a small area.
Reims - research before you get there for when which cellar is open. The cave tours often require bookings. Very much NOT like Napa, cannot just rock up to any cellar door for a tasting, although 'some' do.
The segment you have from Lyon to Dijon I think is my favorite in your plan, the food, wine and restaurants in that segment will satisfy most tastes and budgets. If was to join you I would suggest eating out every night and "back road" exploring by day, buying picnic stuff from road side stalls of the gazillions of little farms all over the area. At what ever is your first stop in France, a supermarket will have enough stuff to make up a cheap picnic kit that can be gifted or disposed of at the end of your trip, just make sure it has a knife strong enough to cut hard cheese, a corkscrew bottle opener, and a couple of wine glass' - a breadboard is good too. Do plenty of research on restaurants in this strip, will be worthwhile.
I know you said museums are not really your thing, but - while in Bayeux, have you heard of the tapestries ? - worthwhile IMO.