I have a vest, that'll do. Too warm for a suit. I'll need to get a bowtie though, regular ties are banned.
Wear a suit. If it's too warm get a cooler fabric than wool or just wear your suit, then take off the jacket when you get there. You'll probably want to wear a pocket square as well (don't match it with a tie and just wear white linen if you can't think of anything). The Tie Bar has a good selection of bowties.
Just wear a black suit (three piece, maybe?), white bowtie, and white pocket square. A hat and cane for more of a costumey look if you want. If you really want to, it looks like they were wearing tuxes in Moulin Rouge, but I doubt you have one of those lying around (maybe just a dinner jacket without matching trousers could work, too, but you'd still need a cummerbund).