The episode title may be a reference to the 1990 documentary film Paris is Burning, directed by Jennie Livingston. The documentary is about the drag ball culture in New York City, and the drag competitions which take place at the balls. The documentary film received rave reviews and several awards at film festivals; it remains relevant in discussions on LGBT, youth, class, and racial issues.
The film’s title comes from drag performer Paris Dupree (1950-2011), who gave a drag ball with the name. It may have been partially inspired by Adolf Hitler’s reported question during World War II, “Is Paris burning?”, when he wished the city to be completely destroyed rather than re-taken by the Allies.
This episode centres on Paris Geller, who we learn more about in this episode, and who does indeed “burn down” or destroy the relationship between Lorelai and Max. She does so to deflect public attention from her own problems, thus playing a role like the drag performers in the film.