You want to dance?
In Europe, many of the serious dance clubs are actually gay. In Paris for example, ' Queen ' 102 Av. Champs Elysees is gay, but attracts a mixed crowd intent on dancing. It's a venue where many top European DJ's spin, Tiesto and the like. It's location and reputation make it pricey.
Don't be put off by the ' gay ' tag ... It started as a gay club and like so many intent on ' dance ' gay clubs are usually where the vibe starts, word gets around and they evolve.
I think they would probably have their own web site, try www.queen.fr ... I think the cover charge is about 20 Euros, I was there last probably 2 years ago.
Sanz Sans is another good one, located in the Bastille area Rue du Faubourg.

In Europe dress code rulez. If you're going to straight clubs expect a degree of clothing snobbery.
I could go on with clubs, but check out http://www.nightfloor.com/boite-de-nuit_paris ... In French but you will get by, it has a day by day listing.

There are a number of bars with either indie type bands of ' dance bar ' categories ... Crowded places would be La Fourmi Ailée, Metro station Anvers.
Les Folies metro station Belleville.

Forget to go to any night club before 1am.

To be honest, it's difficult to give recommendations in a city like Paris because the choice is huge. One thing to remember, it ain't cheap, you'll soon discover.
No doubt you will find yourself on the Champs Elysees at some stage. My opinion it's tack - up there as one of the finest addresses in the world and pure tack.
It will be hard to miss the Buddha Bar on the Elysees. Lots of tourists and outrageously expensive.

3 days is a good duration. You will have the opportunity to see a fair bit. Sample the night life, I hope you find something and some nice French mademoiselles