I think my choice would be a train to Bayeux, visit the tapestry and cathedral there, spend the night, then take a day-long tour of the D-Day sights, or rent a car and drive along the beaches. I think a tour would provide a lot more information and save the driving. Then another night in Bayeux and return via Caen (great WWII museum) or Rouen (Cathedral, Joan of Arc sites).
If you're not that into WWII, then maybe a TGV to St-Pierre-le-Corps near Tours, rent a car, and spend two nights in Amboise or thereabouts, visiting chateaux and such. About two a day would be my limit on a longer stay, but you might manage three on your full day and one each on the first and last days.
Beaune is a good base for exploring Burgundy, and has its own sights, but for me the travel time would be too long to justify just a two-night (one full day) visit. Save Burgundy for when you have more time.
Reims is an easy train ride, great cathedral and interesting Roman gate, plus the WWII museum and all the champagne you want to experience. Two nights and one full day would be plenty.
You might look for Ina Caro's Paris to the Past, her description of a couple of dozen interesting places to visit by train from Paris. Some are day trips, others could be overnight or even two-nighters. She recommends La Rochelle on the Atlantic coast but I haven't been there.