Anything is possible -- but this is where we need to tell you that there are no direct flights, all the trains have to go through Paris, and it's 850km -- about 9 hours of straight-through interstate driving to get from one to another.
Still want to go?
If you are going to Normandy to see the D-Day beaches, you can take the train from Paris to Bayeux or Caen; it's about 2 hours and about 15€ with advance purchase tickets. You can find lots of info on D-day tours on the Bayeux forum.
You would have to chage train stations to make the connection in Paris.
If you are going to take the train, read the posts here about buying tickets on tgv-Europe.com and avoiding RailEurope.
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