1. The Eiffel Tower because you get to see a great panorama of the city. It's usually windy (which makes it feel much colder), so add an extra layer of clothing even if it's nice out.
2. Sidewalk Cafes and Bakeries. Now that France has a smoking ban, sitting inside a cafe won't be as constricting for your lungs, but I still recommend the outside. Watch the people, take your time with a drink. It's heavenly and you won't be forced away from your table if you want to linger. At the boulangerie, order a beautiful dessert for just a couple of Euros, or try a fresh baguette or other bread (pain a la ancienne is good) for under 2 Euros.
3. The Louvre. Plan to spend a day if you like art because in reality you'd need a week. The Mona Lisa is smaller than most people realize. Many great works of art.
4. Le jardin des Tuilieres (might have spelled that wrong, sorry). It's just outside the Louvre and when in bloom, it's a lovely mix of flowers and statues.
5. Versailles. OK, it's outside of Paris, but it's only about a 45 minute train ride, so it's reasonably close. Pictures can't do it justice. Get the audio guide and mosey around at your own pace. It's a good deal to pay for all of the tours.
6. Notre Dame's Bell Tower. Another great city panorama. You have to walk up many narrow winding stairs though, so you need to be relatively physically fit.
7. A walk along the Seine (or a river cruise). Check out the typically Parisian architecture and catch a breeze from the water if it's a warm day.
8. A crepes stand. There's nothing like a fresh crepe made by a friendly street vendor. Start with a ham and cheese (jambon et formage) crepe for your meal. Walk a few blocks. When hungry again, purchase either a Nutella or butter and sugar (beurre et sucre) crepe. Yum!
9. Check out the haute couture shopping on the Champs-Elysees. Also look into Galleries Lafayette, the largest department store in Paris.
10. If you want to see something truly scary and at the same time entertaining, after checking out the Arc d'Triomphe at the end of the Champs-Elysees (there's a pedestrian tunnel to get you there), stop and take a minute to watch the traffic circulating around the monument. It's quite a sight!
I hope you can enjoy the traditional tourist attractions, the everyday Parisian life, and the wonderful food that Paris has to offer.