I certainly second Andi's suggestions above and would add a few more:

Sainte Chapelle - within the Palais de Justice - is astonishingly beautiful, like being inside a jewel box.

The view of the city from the steps of Sacre Coeur is magnificent; and it's fun to eat frites and look at the horribly kitschy "art" in the Place du Tertre around the corner from the church at the top of Montmartre.

A visit to Versailles is a must if you have more than a few days in Paris - try to go on a day when the fountains are active.

The little street market in the Rue de Buci on the Left Bank is a marvelous introduction to the French love affair with good food ingredients.

If you like great kitchen stuff, Dehillerin is a store of pilgrimage.

To see and taste lots of good French grub (and assemble a fabulous picnic for the park or your hotel room), go to the Grande Epicerie de Paris (in a big department store, Bon Marche) on the Rue de Sevres on the Left Bank.

Have fun. Cheers, Fred