There are lots of invasion-related sites in Normandy, naturally. For a different look at WWII, I found the Memorial des Civils dan La Guerre, a museum in Falaise about civilian life and privations during the war, very interesting. It also covers the Resistance. It's quite a new museum, with all or virtually all the information translated into English. I traveled to Falaise from Caen by bus.
Another war-related site is down in Aix-en-Provence, a city-bus ride from the center of town. It's the Camp des Milles, a museum/memorial established at a factory that was turned into an internment camp during the war. People were held there before being sent, by way of the transit camp in Drancy, to camps in the east, I believe primarily to Auschwitz. Again, there is a great deal of English explanatory material in the new museum. I appreciated that the displays went beyond what happened to ask the question of why it was allowed to happen. There is also information about the brave souls who risked their lives to save others.
Most of the one-day small-group tours of invasion sites originate in Bayeux, which is more picturesque, overall, than Caen. Most of Caen's historic architecture was obliterated during the war, whereas Bayeux survived basically unscathed. In Bayeux you have several worthwhile sights in addition to the historic center itself: the Bayeux tapestry, the cathedral, the invasion museum, and the British cemetery.
Caen is a more convenient bases for side trips by public bus or train. It may or may not be advantageous for you to stay there since you plan to have a car for part of your time in Normandy. The very large Caen Memorial is a museum that spans the period leading up to the war, WWII itself and the Cold War. It's a full-day place if you want to see all parts of the exhibition and read most or all of the posted information (again--overwhelming available in English). I liked this museum, but other folks justifiably find it large, crowded and expensive. It's not located in central Caen, but it can be reached by city bus.
Also in Normandy is Rouen, with its beautifully rebuilt (after wartime destruction) historic center. It's served by trains from Paris.
I found Marseille's museums really disappointing, but the historic area around the Old Port is attractive, and the hilltop Notre-Dame de la Garde is impressive. Notre-Dame's English website isn't working for me at the moment.
It might be as easy to visit Aix-en-Provence by bus (faster than the train in this case, but train would work, too) while you're in Marseille than by driving from Avignon. Car Treize runs multiple buses per hour to Aix; it looks like two of them are expresses taking just a bit over half an hour each way. The drive from Avignon would take over an hour each way, not counting the time you'd probably spend looking for a place to park the car (and possibly walking some distance from that point to what you want to see).
