I'm having difficulty assembling an itinerary from Paris to Caen (?) via train, then D-Day Full Day group (not private) tour, then Caen to Paris via train, arriving back in Paris no later than 21:00. My check of trains departing Paris for Caen indicates they arrive in Caen around 9:00 am, but I believe the full day tours begin around 8:30 AM. Can this trip be done in a single day from Paris? We don't mind departing Paris early am. Which of the tours offered will coincide with the train schedule and be the most informative.
Your plan is not really the best. You'll need at least one night away from Paris to do a full day D-Day tour. When my wife and I did it last year, we caught a morning train to Bayeux, saw the tapestry (not to be missed!) spent the night there, and took a full-day tour the next day. The tours usually finish up at about 5:30, and you can get a train back to Paris about dinner time. The train trip Bayeux-Paris is only about 2 hours. Before you get on the train, get a sandwich and a drink to go, as there is no snack bar on board.
Jon, I definitely agree with the previous reply! Given the train departure times and other factors, it's very difficult to get to Bayeux in time to join many of the tours as they usually depart precisely at 08:00. Keep in mind that you'll need to get from whichever area of Paris you're staying to Gare St. Lazare, which is where the trains depart for Normandy. Spending at least one night in Bayeux and returning to Paris after the tour is really the best idea (and as mentioned, this would also allow you to see the famous Tapestry which describes a much earlier battle). On arrival day, you could also visit the WW-II Museum in Bayeux. One native would be to take one of These Tours however they're a bit on the "pricey" side and would only allow a brief view of the landing sites. Happy travels!
Don't think most Americans realize just how massive the D-Day Beaches are over 50 miles from one end to the other and not including areas behind the beach. About the only way to see them in a day is a tour from Paris but you send a lot of time on a bus that way. And then those tours just give a snapshot. See them at all well, as others have mentioned, is an overnight. It you cannot do that, then save it for another trip.