I've never been to Italy but I did visit Paris for 10 days a few years ago, so maybe I can help.
We stayed at the Hotel Elysees which a block down from the Arc de Triomphe. If you've never stayed in a European hotel in a big city be prepared to see the tinyest room you've ever seen, but it'll be clean, quiet and have everything you need. The Metropolitain is the subway system and it's great. There's a main hub under the Arc and you can go anywhere in the city from there.
If you're on the Champs Elysees - and you should be - make sure to have dinner at the Sebillon Elysees. Fantastic French restaurant and even a semi-picky eater (like me) can find plenty to enjoy. If you don't have the profiteroles for dessert, you're missing out.
The Arc de Triomphe, Louvre and the Eiffel Tower are must visits, of course, but Sacre Coeuer and Hotel des Invalides (Napoleon's tomb) are interesting as well. If you're into creepy history check out the catacombes (I did), too.
Everyone will tell you to visit Notre Dame, and for good reason, but I was more impressed with the Cathedral de Notre Dame in Reims. Where is Reims? About a 45 minute train ride into the Champagne region. Tour one of the wineries and sample the wares while you're there.
We also took a tour bus into the country to visit Monet's home, and the gardens made famous in his paintings. Didn't do much for me but my companion found it romantic and she made me appreciate it more as the day went on.
Warning: if you don't speak French, stay in Paris where English will work just fine. In Reims, I encountered language barriers that would've been a problem had my travel partner not been fluent in French. (For a moment just now, I actually missed her) :p
Hope some of that is useful. Have a great trip and if you have a question, just ask.