What is the best mode of transportation to go from Paris with a stop in Giverny, and then on to Normandy to see the D-Day beaches and spend the night?
The train. The stop for Giverny is actually in Vernon. There will be a bus waiting outside the station to take you to Giverny. Where in Normandy do you want to go?
Honfleur, Trouville, Deauville, Bayeux. In other words, visiting the towns near the D-Day invasion, and the US cemetery.
You would be better served with a rental car. We always train to Caen then pick up our car there but many can book a car at CDG or in Paris, drive to Giverny, thence on to Bayeux. With a car you can see all the towns and sights at your pleasure and driving in France is very easy. You can also zip over to Mont St Michel with your car and arrive before the tour buses, spend about 2 hours tops at MSM then return to Bayeux to view the famous tapestry. Get a car.
George is correct that a car would be better for all those stops. I got the impression from your question that you were just wanting to go to Normandy and would be taking a tour. My bad!! I would not recommend you pick up a car IN Paris. Get it at the airport or on the outskirts of town. I can't remember if they have a left luggage facility in Vernon. If they do, you could take the train there, then on to Rouen to pick up a car.
Thanks for the advice @ the car and also recommending Mont St. Michel. Getting a car in Vernon sounds good so I'll check out if they have a place to keep luggage while touring Giverny.
Nancy, if you pick up the car in Vernon you can put your luggage in it and drive to Giverny. Just make sure the luggage is out of sight.
Nancy, much good information already ,particularly from George but allow me to add my deux centimes . Coming from Paris to Normandy last fall we trained to Rouen and picked up the car there as we wanted to see the old town and Rouen cathedral ( Monet fans , as well ) We had considered Giverny but since we wanted to spend the afternoon in Honfleur we decided to forgo Giverny this time around . Our thought was all three in one day would amount to checking off boxes. Certainly , this is a matter of personal consideration . Honfleur was wonderful and I have long wanted to see it as so many impressionist painters went there to work . Honfleur is not directly accessible by train and therefore without a car would have been somewhat impractical ( not sure about trouville - deauville ) . But as George and others have said , however you do it , a car is essential for touring the D Day sites and the driving there is most pleasant . Have a great time!!