Dress warmly. Turtlenecks are always in style. Wear comfortable shoes...bring 2-3 pairs. The last thing you want or need is a blister on your foot. Wear a moneybelt or a neck pouch...keep your passport, credit cards, cash, etc in there for safe-keeping. Operate with a day's spending money in your wallet. Bring a scarf (or buy one there...Rue de Rivoli has great deals) and gloves. Wearing jeans is fine...I would not recommend bright white tennis shoes though.
Be courteous and polite. When you enter a shop, say "Bonjour" and "Au revoir" when you leave. Get a French phrase book (French at a Glance is great!) and memorize some key phrases. If you at least make an attempt to speak French, the Parisians will appreciate it. Sometimes they will start speaking English to you. Use "s'il vous plait" (please) and "Merci" (thank you) a lot. Read the phrase book on the plane ride over.
I don't know if you have a Paris guide book yet (I'm sure you do), but I'd recommend Rick Steves' Paris 2007. Great book, great tips. There are some tours of certain places, including the Louvre, Versailles, Musee d'Orsay, etc. You can also download (on his web site) some of his tours to iTunes and then to your iPod and do a hands-free tour.
If you plan on seeing a lot of museums, get yourself a Museum Pass. You can purchase them at certain Metro stations...saves you a lot of time from standing in long lines. I'm not sure how long you'll be in Paris, but either a carte orange (good Mon-Sun for unlimited Metro access) or a carnet of Metro tickets (10 tickets) for your transportation.