I appreciate the help and expertise!
What's a "must see" really depends on your personality and interests and to an extent exactly when you're there and can travel. I lived in northern Italy for over 13 years and traveled throughout Europe at every opportunity. In my experience, there are interesting things to see & do, good food and nice people just about anywhere you might go. That said, I can highly recommend visiting the Netherlands especially if you're there in late April when the tulips are at their peak. Depending on where you are in Italy, it's not all that difficult to visit Italy. The night train from Paris to Venice is a good way to get there. You can sleep through the night, arrive early in the day and not have to pay for a hotel/hostel the night you travel. You can also connect in Milan to trains to Florence, Paris or anywhere else in Italy. Barcelona is also a relatively easy trip as are Brussels and London. Bruges is a wonderful place to visit. Prague, Vienna, Copenhagen, Stockholm and Budapest are wonderful, but further from France. Of course, there are lots of interesting things to see in France. Visit Monet's garden in Giverny, Mont Saint-Michel, Eze, Carcassonne or many other options.
Here are some resources that can help you plan and check options and current prices for your trip (expect prices in the future to rise):
http://www.skyscanner.it/ - particularly good for budget flights within Europe, but you can also use everywhere as a destination to do something like the explore option on Kayak. You may not need the airfares, but you can compare to the cost of the trains to get around. this one may be more useful for you.
http://www.seat61.com/ - a great train site with details about railpasses. It can be cheaper to buy individual tickets than passes. This site will tell you how to determine whether you're better off with a railpass or individual tickets or some combination for your trip. It also details how to use the pass and what to avoid to get the best use out of a pass.
http://www.venere.com/ - hotels/B&Bs - prices for the same hotel can vary hugely depending on the season and what local events are going on.
http://www.hostelbookers.com/ - hostels.
http://www.monasterystays.com/ - monasteries & convents that offer accommodations
http://www.venere.com/ - hotels/B&Bs - prices for the same hotel can vary hugely depending on the season and what local events are going on.
http://www.hostelbookers.com/ - hostels.
http://www.monasterystays.com/ - monasteries & convents that offer accommodations
Where you go depends on how much time you get off from your studies, and your budget. Just have a look at a map of Europe and decide where you want to go, within your timeframe, and what you want to see. Surely you can find plenty of information on the Internet regarding countries close to France. You also do not mention just where in France you are studying, and that makes a difference to where you go due to the distances involved.
Sounds like you are simply looking to do the bragging rights thing, and not actually learn something. Do your own research, you have an infinite library at your disposal.
Go almost anywhere!!