Any suggestions on taking a day trip from Paris to Normandy by train.
Normandy is a rather large region. What places in Normandy are you interested in?
If you are wanting to see the WWII sites, either go to Caen or Bayeux by train. If you just want something different from Paris, you could take the train to Rouen. Look up Rouen images to get an idea of the quaint historic center which is an hour & 15 minutes by train,
This is asked a lot on this forum. Most people who have actually been there would recommend going when you can spend way more than one day—minimum two nights. If you are talking about the D-day area, that is 3 hours minimum each way from Paris (2+ for the train, and another bit of travel to get to the beaches from the train in Bayeux or Caen—from where you will initially arrive). And that is assuming you are already staying near the Gare Saint Lazare train station in Paris. Plus, there is no realistic public transportation to/from the D-day beaches. The place deserves more than a photo op.
You need to send the night in Normandy. Also, if you go, see the D-day beaches, American Cemetery and Bayeux.
Don't miss the Bayeux Tapestry, the 900 year old tapestry that tells the story of the Norman conquest of England. It is amazing. It looks like it was made yesterday.
I agree that one or more nights in Normandy is highly advisable. There's a lot to see up there even if your only focus is D-Day sites and museums. However, Overlord Tours offers a full-day tour for people taking the early train up from Paris. The tour picks up and drops off at the Bayeux train station rather than the usual meeting point in the historic center. Note that if you opt to do this, you won't have time to see Bayeux at all.