overnight trip from Paris

To give you more specific advice, could you clarify how much time you actually have for sightseeing in the place where you would do the overnight trip?

Normandy is definitely worthwhile. Take the train to Bayeux (going through Caen), spend the day sightseeing in town and visiting the Bayeux tapestry. Spend the night and then get a tour out to the D-Day beaches the next day. When the tour is over in the afternoon, catch the train back to Paris from Bayeux (transfer in Caen). Or, if you really want, the TGV can have you in Strasbourg in four hours. Leave Paris early one morning, get to Strasbourg by noon, spend the afternoon in the city (Petite France is especially worth a wander), eat dinner in a winestub, and then take a tour down the Alsatian wine road the next day (stop in Colmar). Honestly, with the TGV, there are lots of places within easy reach of Paris, though many (Normandy and Alsace included) deserve more time. Still, you get a taste of something outside of the city!

Yes, there are a world of possibilities - as previous posters have noted you might want to consider:

Time
Cost
Ambience
Pace

For instance, you can take the RER out to Chantilly and Senlis. Very inexpensive, less than an hour both directions. Nice slow trip where you can explore and get into the village a bit, very relaxed.

Or you can hop the TGV for Strasbourg or Avignon (or Nice or many other destinations) travelling at 300 kph, jump off, race around, spend the night and return. High speed, fast paced.

Or virtually anything in-between.

You can go virtually anywhere in a day trip from Paris, and virtually anywhere you go in France will be absolutely terrific. So you'll need to decide what you are looking for and what interests you the most.

For more ideas, Annebel Simms wrote a wonderful book "Day Trips from Paris." I found it at a used book store, but probably through Amazon as well. These are ideas for some famous and not-so-famous day trips.