I went to France for the first time last summer, and it was amazing! Paris is wonderful, obviously, with SOOOO much to see and do. We also took small day trips to Giverny (Monet's home and gardens) and Versailles. My group also went to Tours (and saw several castles in the area: Chenonceau, Chambord, and Amboise - very neat), Sarlat (beautiful little town), Rocamadour (little town perched on the edge of a cliff overlooking the Dordogne Valley), Oradour-Sur-Glane (very sad but an amazing piece of history), Carcassonne (medieval ramparts), Aigues Mortes (another medieval town), Montpellier, Nice & Cannes (both BEAUTIFUL) and Monaco (also extremely beautiful)..
We were there for 10 days and really jammed each day with so many different cities and sites. I feel like I really was able to experience France, although there is still so much of the country that I haven't seen. I would recommend every place that we went, but if I had to pick only five cities, I would choose Paris, Sarlat, Oradour-Sur-Glane, Cannes, and Monaco (technically its own principality).
EDIT: If I had to pick the top 5 sites, they would probably all be in Paris. I would pick the Eiffel Tower, the Louvre, Arc de Triomphe, Sacre Coeur (and the amazing view of Paris), anddddd... probably Versailles, which is right outside of Paris.
Went to France last summer and going again in 2 weeks! :)