I really must do an intro, this is my second de-lurk! I assume you are wanting to shop for clothes/shoes? Anything else specific?
There is really great shopping all over the city, so just about anywhere you go you are going to find something. I used to live there, but it's been five years, so I don't want to recommend specific shops in case they have closed/moved. Except, of course, for the department stores, which are fairly near where you will be. Since you only have the one day, you might try those as you'll get one-stop shopping. Galeries Lafayette, Printemps, and Samaritaine are the classic three. There are a multitude of small boutiques in the same general neighborhood. On the rue de Rivoli between Samaritaine and the Louvre is also where you'll see C&A (Dutch, fun, low priced) and probably an H&M, with many more shops interspersed. Monoprix is like a French version of Target, although only the big stores -- there are some Monoprix that sell only groceries. Lots of shoe stores along there if I remember correctly. The area around the dept. stores and on the rue de Rivoli is also the most crowded shopping area of the city, I think, especially during tourist season, so be ready for that.
I like the whole area around Madeleine, rue Tronchet, rue Cambon, boulevard des Capucines, avenue de l'Opera, boulevard Haussmann (where Galeries Lafayette and Printemps are), etc. On the other side of the river, I like the triangle bounded by boulevard St. Germain, boulevard Raspail, and the rue de Rennes (esp. this street). There is a small department store (read: less crowded) just off the boulevard Raspail called Le Bon Marche (Sevres-Babylone metro stop; there's a lovely small park there as well).
If you want to ogle the designers, try the avenue de Montaigne just off the Champs Elysees, metro stop Franklin D. Roosevelt, or Place Vendome (very close to the Louvre). Avenue de Montaigne is jam packed with the biggest names in fashion, while Place Vendome is a small collection (Chanel, Cartier, Phillipe Patek, Rolex, Dior...). I never did go into any of those, but it's fun to "leche les vitrines" (window shop, or, literally, to "lick the windows").
Right now (lucky you!) -- through the beginning of August -- Paris is having "les soldes" -- big sales everywhere you go. Every store will have a "soldes" sign in its window. The downside to shopping there right now is going to be the heat. Air conditioning is rare, even in hotels and stores, and the crowds can easily overpower what meager air conditioning the stores provide. If you need a blast of AC, go to a movie or pop into a florist shop.
Random tips --
Go early to the department stores, as soon as they open. It will be cooler and far less crowded -- the French do not shop early.
Stores in France are required to display prices on merchandise in the windows, so checking those before you go in can be a good way to gauge whether it's a store you can afford.
If you see a clothing store called a "depot vente" it is a consignment shop, by all means go in!
When you walk into a small shop or into a section of the department stores, make a point of saying "bonjour," or even better "bonjour madame/monsieur" if you can manage it, to the shop personnel, and "merci, au revoir" as you leave. This is an expected courtesy in France and you will get far better service with this small habit (really, no matter where you are -- metro ticket window, on the bus, at a bakery, checking into your hotel -- always say "bonjour" first).
Oh, and if you'd like to pick up a book/magazine in English or just go somewhere you can ask a question in English, stop into the WH Smith on the corner of rue de Rivoli and rue Cambon, or the Brentano's on the avenue de l'Opera, both are English-language bookstores.
I hope that's helpful -- it is kind of hard to narrow down since there is so much there, but that should give you some starting points!
