Le Crocodile, Paris
At 2AM, in case you don't have enough with the Pantalon, (see above), you can cross the street and go to the Crocodile.
The Crocodile is a cocktail bar open from 10PM to 5AM. They have a long list of several hundred cocktails, with and without alcohol (but who goes to a cocktail bar at 2AM to drink non alcoholic cocktails anyway). The atmosphere is very friendly, but the place is packed because it's open after 2AM, when most other bars close.
It is not cheap, but you'll have your money worth. It is not a trashy dive either, being in the posh Latin Quarter district.
Dress Code: Anything goes.