car rental or public transportation

No. Basically, there is little to in some cases no, public transportation to the D-day sights. You will need a car—either one of your own, or that of a guide.

Phil

If neither you nor anyone in your travel party is an expert on the invasion, I highly recommend taking a small-group D-Day tour. A lot of the tours originate in Bayeux and use vans. The driver/guide will provide a lot of background information, even as you are driving along, and you will learn a lot more than if you just drive around. You'll also cover the ground a lot more efficiently.

Between Bayeux and Pontorson (train station closest to MSM), there's generally only one direct train per day that's convenient (e.g., that's not at 6:24 a.m.). From MSM back to Paris, there are more connection options. But I'd still prefer to have a car for a good portion of the route.

We had a rental car for the area-Honfleur, Bayeux, MSM but booked a guided tour of DDay beaches with Bayeux Shuttle. It was excellent

Yes, you can do it without a car.

Base yourself in Bayeux (easily reachable by train from Paris Gare St Lazard) and engage the services of a D-Day guide to take you on a one- or two-day tour of the battlefields and cemeteries etc (to my mind this is preferable to driving yourself unless you are virtually a WWII expert — the knowledgeable guides will enhance your experience immensely, teaching you about the big historical outlines of the engagements, as well as engaging details of particular soldiers and units).

If you stay at the Churchill Hotel (or maybe even for non-guests?), you can take one of their shuttles for a day's visit to Mont St Michel.

http://www.hotel-churchill.fr/en/shuttle-bayeux.html

To visit Giverny, you can take the train from Paris to Vernon and then the shuttle for a day trip from Paris.