Even in July the weather in Normandy tended to be overcast, and virtually every day brought the possibility of rain, though usually not all that much actually fell. The meteorologists seemed not be able to predict precipitation with much accuracy. It can also be quite windy, especially along the coast, so I agree with the suggestion often made here that travelers rely on hooded waterproof jackets rather than umbrellas. I haven't traveled in Europe beyond mid-October so can't provide first-hand information beyond saying that you should probably expect damp chill if you're lucky and damp cold if you are not. If your raingear is windproof, that will be very helpful.
Check ViaMichelin.com for driving times (recognizing that they are optimistic and do not factor in any stops, getting lost, searching for parking, etc.). Compare those times to the rail schedules on sncf.com. I think you'll find that for your destinations, the train will get you to the area faster. Whether a car will be useful once at your destination will depend on what you want to do upon arrival.
I'm not sure how picturesque the little Norman towns will be in late November, and I'm of the take-a-tour school of thought where the D-Day beaches are concerned. You would surely see far less in a single day of driving yourself around. There is rail service between Caen (huge WW II museum) and Bayeux (origin point for many of the van tours, and home of the Bayeux tapestry and a smaller D-Day museum). There is transportation along the coast in both directions from Caen, but it can take a while to reach the farther destinations without rail service.
In southern France a lot of attractions cut back their hours of operation and even days of operation in the off-season. If you're mainly interested in the major sights (like the Palais des Papes in Avignon), you'll probably be OK, but it would be best to Google for the individual websites and check the schedules. I think there are some less mainstream places that may be closed Mon-Tues or even Mon-Wed. I think Avignon is a large enough city that it will remain pretty lively in November. Incidentally, the Palais des Papes (which is unfurnished) has an exhibition of contemporary African sculpture running until January 2018. I felt it added a great deal to my visit.
Strasbourg is huge and shouldn't be an issue in terms of availability of sights and services. Colmar probably also gets significant tourist traffic all year round--justifiably, because it is gorgeous. Check the schedule to be sure you have an opportunity to see the Unterlinden Museum in Colmar. The Isenheim Altarpiece is one of those you-really-should-see-it artworks, and the rest of the museum is worthwhile as well.