Hi Ellen, we did a day trip from Paris to Normandy last May. It's an interesting area with lots of history, and it would be better if you had more time, but if a day is all you have, it can be done.
We took the train and arrived in Bayeux at noon. We had a quick sandwich at the cafe across from the train station (there's not much in walking distance). Normandy Sightseeing Tours (http://www.normandy-sightseeing-tours.com/) picked us up at 1 p.m. You need to make reservations in advance. We did a 5 hour tour, and they dropped us back off at the train station. We took the 6:30 p.m. train back, and arrived in Paris at about 9:30 p.m.
It was a nice (quick) overview. My friend hadn't been there before, but was satisfied with what we saw - Omaha Beach, the American Cemetery, and a bit of the surrounding area. Actually, he says that day was one of his best memories of the trip to France.