I am a big proponent of a D-Day tour for folks who don't have a member of their travel party who's an expert on the invasion. The van tours have driver/guides who are experts and will move you around efficiently while providing historical background. I can't imagine the typical tourist who just shows up in a car gets as much out of his time along the coast as those with a good guide--and I am not a big user of tour guides in general.
You can take the train from Paris to Bayeux, which I consider by far the best base for exploring D-Day sites without a car of your own. Bayeux has nice sights of its own, the major ones being the tapestry, the cathedral, the invasion museum (newish and very good) and the historic center.
It's possible to get from Bayeux to Mont-St.-Michel by public transportation, but it isn't particularly quick or easy. You could rent a couple of cars (there's one agency in Bayeux, more in Caen a short train ride away), or you could check out the day-trip run by the Churchill Hotel in Bayeux. I understand you can take that trip even if you are not staying at the hotel. However, folks who've been to MSM recently report that it is a mobscene during day-tripping hours and highly recommend arriving late in the afternoon, spending the night either on the island or on the mainland, and departing mid-morning the next day. I am not speaking from experience because MSM has never been important enough to me to justify the hassle of getting there.
If you decide to rent a car or cars, you should make those arrangements before you leave home. Many folks recommend working through one of the consolidators (AutoEurope, Kemwel, Gemut) for possibly better rates, useful information, and support if something goes wrong. This is another thing with which I have no experience, but I know AutoEurope has been recommended by multiple guide books for decades.