Nightlife can be extremely expensive and/or snobby in Paris, but go to the right places and you'll be ok.
First off, there's no First Amendment right letting people go wherever they want. If your clothes and shoes and appearance aren't right - of if they don't like your race - they can keep you out of a nightclub. Most of them employ a physionomiste who knows what to look for, who looks like they belong, etc. So even your overcoat has to look sharp while you're standing in line. The best bet to get in is to tell the bouncer that you'd like to buy a bottle. You pay a good chunk of cash in advance and you're pretty much guaranteed admission.
But at 12e a drink and with a 20e cover, you're better off skipping the well-known clubs and heading to either student-oriented bars (check out La Leche Vin for cheapies and young hotties), mixed/gay clubs (far more tolerant at the door), and DJ bars, basically a bar with a dance floor - and better yet, no cover.
My personal favorites are a DJ bar called Wax in the Bastille on Rue Daval (hard to find, ask around...). Nearby it is a great dive bar called Fleche d'Or - if you go, make sure you check out the bathroom. There are also some great, divey bars in the upscale St. Michel/St. Germain area just south of Notre Dame. You can find litre beers there for under 6e, and some places for less, which - believe me - can be a bargain.
Mixed drinks SUCK. They charge you about 8e for a tiny-barely-one-ounce shot and a few euro more for a mixer, so if you can take a hipper with you, go for it.
Most of the music you'll run into is funky house. The French LOVE their house, with a tinge of disco. There are some rock and hip-hop clubs here & there. Check out clubwear stores (there should be a handful around the Les Halles shopping area) for flyers.
The best approach you can take is to chum up with some locals or people who've been staying there a while and see where they take you. Bonne chance!