I will have a free weekend in Paris (will be there on business). Have been in the past and have seen the major sights. Was trying to figure out the best way to spend my time. Was thinking of doing a deep dive into Paris on Saturday (cafes, walking around, soaking up the city) with a day trip on Sunday (last time in Paris on Sunday, many things closed). Was thinking of a trip to Versailles. In reading, Normandy may not be possible. I would rather go see the D-Day beaches, if possible and just try to get an understanding if possible.

There are tour operators in Paris who go to Normandy... don't know how good the tours are..

Paris Vision
Cityrama

Normandy (Arromanches & landing beaches) are a very worthwhile trip. Perfect for a quiet Sunday. The WWII museum in Caen is magnificent. Every American should see the American Cemetery in Normandy.

Book before you go. Try :

http://www.linkparis.com/daytripsfromparis.htm

http://www.daytripsfromparis.com/

http://www.linkparis.com/normandy-day-tour.htm

It's a very nice drive if you feel in the mood for renting a car. You could stop and see Rouen on the way back.

What about other places that may be a bit further out? Brussels? Nice? I have been to Europe a couple of times and only have beeen to Paris, London and Munich. Is this an opportunity that I should take to see somewhere new?

Not in a day! I'd stick with Normandy.