Daniel, your best bet is to travel by train from Paris to Normandy. The train for that area leaves from Gare St. Lazare, as I recall, which is easily reachable by Metro.
If you're planning to visit WW-2 sites, then I'd strongly suggest spending at least a couple of days there. Bayeux is a good place to use as a "home base". As others have suggested, BattleBus Tours are superb, but as these depart at about 08:00 they can't really be done as "day trips". The information they provide and some of the "special sites" visited on their tours are some of the best memories of my visit to Normandy! I took both the U.S. highlights and Canadian highlights tour (two days, as they're about 9-hour tours), and both were excellent!
It's certainly possible to rent a Car in Bayeux if there are specific sites you want to access. I rented a car for one day to visit Longues sur Mer and Pegasus Bridge. There's a rental agency not far from the main square. The Hotel owner kindly set up the rental for me, as the people at the rental agency don't speak much (any?) English. I was able to get through the rental process with my "rusty" high school French, but wasn't exactly sure what I was signing! A good map or a portable GPS unit would be a good idea!
Good luck and happy travels!