There are so many! If you have a big budget, then of course head to Rue Saint Honoré and Rue du Faubourg Saint Honoré, where the famous fashion houses have their boutiques, e.g. Chanel, Lanvin, YSL, Chloé. Even if you can't afford to shop here, it's great to just walk down the streets and see all the amazing window displays.
If you're not looking to spend so much money, there are less expensive but still very French shops. Good ones are APC, Comptoir des Cotonniers, Sandro, Maje, Isabel Marant and Vanessa Bruno.
There are obviously the standard high street stores, like Zara, H&M, C&A and Camaieu, but if you want to get something special that you can't find anywhere else, these aren't the places to go.
If you're a fan of vintage, there are a lot of great vintage shops in Paris. Here are a few of my favourites:
32 Rue des Rosiers 75004 (this one doesn't have a name, it just says 'Coiffeur' over the door)!
Free'p'star - 8 Rue Sainte Croix de la Bretonnerie or: 61 Rue de la Verrerie, both 75004
Kiliwatch, 64, Rue Tiquetonne, 75002
It's also always worth a visit to the famous flea market Puces de Vanves at Avenue Marc Sangnier and Avenue George Lafenestre 75014. It's open from 9 till 1 on Saturday and Sunday.
Also, make sure you visit the famous department stores Galeries Lafayette and Printemps - they are both amazing just to walk around, even if you don't buy.
Hope you have a great time in Paris!