Paris is lovely. I do get a bit frustrated with it however. France has so much beauty, but a very large area around Paris is very flat and boring. If you just stay around Paris, I think you'll find yourself saying that Europe is ugly.
If you're staying a week or more, you'll have time to drive around. I suggest heading east and hitting:
Strasbourg, FR. It used to be German but the wars pushed the border around. Lovely town and you'll be hard-pressed to find nicer people.
Heidelberg, GE. Neat old castle with terrible german wine. Lots of old-meets-new.
Dinkelsbuhl, GE. One of the older towns that still has its original medieval wall surrounding it. Every single night since the 1400s, a bugler walks the wall and sounds the all-is-well call.
Munich, GE. This is germany in a nutshell. It is iconic.
Saltzburg, AU. The salt mine tour is so much fun. The Abbey is remarkable. Not to mention, the drive from Munich through Bavaria will transport you to every Disney animated movie from the 40s. You'll feel like Snow White and Sleeping Beauty all at once.
Wind your way down through Lienz and cross over the Dolomites into Cortina, IT. Ridiculous beauty crossing the alps.
Venice, IT. Because duh.
Milan, IT. What an amazing old town. Do the rooftop tour of the Duomo
Head up through the interlaken region of Switzerland and then tell me how much you feel like coming back for Christmas.
If you want to go further north, this loop will be more historic and less whimsical, but still lovely.
Head up to Brussels and the Hague, then up to Amsterdam. Cross into Germany and do Hamburg and Berlin. Swing back through Frankfurt and Dusseldorf, OR... continue on south east and do Prague CZ, Vienna AU, and the Budapest, HG. Then fly out of Budapest.