Yes.
Several images (i.e. clowns, men in tuxedos with tutus) are taken from Toulouse-Lautrec's paintings of the Moulin Rouge and nearby clubs. Some of Lautrec's lines in the scene after Satine rejects Christian are taken from his letters.
Frenchman Henri de Toulousse-Lautrec is played by Hispanic (Colombian) actor John Leguizamo. In the 1952 film Moulin Rouge (1952), he was played by another Hispanic actor, Puerto Rican born José Ferrer. Cast member David Wenham shares the role of another Frenchman with Ferrer: Cyrano de Bergerac.