And finally, the book pairings I think share some thematic resonance with Moulin Rouge. A particular caveat. I do not read a whole lot from this particular time period, so I'm focusing on other aspects.
Heidi Helig's For a Muse of Fire has theater, and performance, and trying to survive. The story also includes ephemera including scripts of things that are happening.
Lucy Parker's Act Like It has characters finding lines blurred between their stage relationship, their staged relationship, and their actual relationship.
Rebekah Weatherspoon's Treasure remains a delight I continually recommend for the story of a stripper and the woman who can't keep her eyes off her, for it's discussion of artistic expression, class difference, and depression and what that means for your love life.