France

First place, maybe Rick didn't tell you this, but there is no such thing as "Euro Rail" (sorry, Virginia). Eurail is an organization put together by the national railroads of Europe to package and market rail passes. The trains in France are run by French Rail, SCNF. I'm no expert on French Rail, but I don't think there is good rail service to Normandy. You'll probably have to go part way by train, then by bus. That probably makes it too long a trip for a day trip. I'm sure one of the France experts will tell you more.

You could make it an overnight trip as there is more than enough to see; you could rent a car and drive it yourself for either a very long day or a pleasant overnight. How long to stay depends on what you want to see in Normandy.
WWII sites and museum, the Bayeux tapestry, Honfleur, etc...?

In my opinion, Normandy is too long a trip for one day. And it is best seen by car. The D-Day beaches alone are most of a day. By car.

Elizabeth: Doug and Melissa have nailed this one. My concern would be that with only five days in Paris, you might not want to take essentially two days out to see Normandy. If you want to do a pure daytrip from Paris, there are lots of options...Versailles, of course, is the most obvious. If you are already planning on doing Versailles, you might consider daytrips by train to Chartres for the great cathedral, or Reims for the cathedral plus champagne-making tours. Either would be only about an hour out and an hour back. Or, depending on where you go after Paris, you might stopover...for instance, Strasbourg on the way to Germany.

If you drive, since you have 2 - 4 drivers, you could wake up very early, immediately rent a car and drive out of Paris on good roads, see the beaches and the American cemetery ( or Canadian) possibly the museum, and return at night. But, you would be missing Mt St Michel, the Bayeux Tapestry, the charm of Honfleur, the Cathedral, Giverny. Did not check the fare for 4 of you to take a train and then rent the car as previously suggested; it might be faster to rent the car once out of the city, but less convenient. You would have to run the numbers and decide. Look at Europecar for a quick car rental quote and find a renting facility hear your hotel to start. Have fun! One of my teens appreciated seeing the Normandy beaches after seeing the D Day museum in NOLA.

Where are you going after Paris? There is a beautiful American cemetary in St. Avold on way to Germany and Strausburg is lovely canal city if you are headed to Germany. Let us know what the rest of your travel plans are.

What exactly did you have in mind to do in 'Normandy'? For instance, there's a beautiful American cemetery - WWI & WWII - on the outskirts of Paris. Or, do you just want to see the completely unique architecture, and walk around a representative town? If you want to see a bunch of WWII sites, you really need AT LEAST 2 nights/2-3 days there, and a good plan &/or tour guide. An overnight trip is an absolute minimum. I wouldn't bother with it...and lose 1 or 2 days from Paris!