The Galeries LaFayette is a must-go! I did most of my shopping here and at the adjacent stores in the area. The building itself stunning. It's not only a department store, but it's historic and grandiose. You can find basically every name brand that you're looking for, and Galeries LaFayette offers selection from all the leading house fashion brands, such as Fendi, Dior, Longchamp, and much, much more.
Just down the street from Galeries LaFayette is Citadium, which offers a mix of high fashion brands like The Kooples, to popular brands such as Adidas and Fjallraven, to more afforable and fun options, like Pull and Bear (a Spanish line similar to Forever 21).
Les Champs Elysees
One of the most famous streets in the world, les champs élysées leads up to the magnificent l'arc de triomphe (which you can go up, by the way). The street is lined with some of Paris' most reputable and coveted fashion houses, such as Louis Vuitton (this location is also like a museum), Guerlain, Cartier, and much more. Laduree (which I also write a post on here) is also on Les champs élysées.
Les passages couverts
A little hidden treasure, the covered passages have stores, bakeries, and restaurants. They're a great discovery and fun to go through. They were built in the 18th and 19th century as a precursor to our current day malls.