In France, shopping more or less means : buying clothes. Assuming that's what you mean't :
My advice : go to the left bank, in the saint-germain des prés area :
Strioll on rue de rennes, rue de grenelle, rue du Four, rue de Sèvres, rue du Cherche-midi... There, you'll find a mix of smalll and big designer's shop, brand shops, and bigger places like H&M (rue de rennes), Zara (rue de Sèvres)... You can also educate your eye at the Bon Marché on rue de Sèvres : high-end grand magasin. Much more parisian than the hausman grands magasins which are for tourists. More expensive, too. Don't miss the grande épicerie and the floor above it which for younger (and no less expensive) designers.
http://www30.mappy.com/sid2SvbKFH3Jy7Mn21w/cFGM?recherche=0&posl=poi&show_poi=0&show_iti=0&poix=0&poiy=0&poi_rr=0.5&poi_rx=0.6&poi_ry=0.5&csl=poi&fsl=m2&gsl=m2&msl=m2&temp_no_prop=0&comment=&xsl=plan&out=2&lr=0.5&force_radius=&wcm2=&nom2=&tcm2=&a10m2=&xm2=&ym2=&wnm2=rue+du+four&tnm2=&pcm2=75006&scm2=&ccm2=250&com2=EU&x=27&y=5
if you go there, you'll be among french chic shoppers (same with the Marais & rue des Franc-bourgeois, less upscale but style "tendance" but I don't know the area as well).
Champs Elysées is for the tourists and the suburbs.
Avenue Montaigne and rue du Faubourg saint-Honoré are woth going to if you are interested in fashion. The top end designers and haute-couture.You can't afford ANYTHING, and it's quite intimidating to go inside, but if you're not shy, what the hell, and if you are, there are still the window to look at !