The saying is "I couldn't care less." If one were to say "I could care less," that conveys that one DOES care, as it is POSSIBLE for one to care less. If one could not care less, then obviously, one does not care at all.
Also, the first word of the title "Moulin Rouge" is not pronounced "moo-lawn." The closest approximation I can type in English is "moo-lain," but with the French near-silent pronunciation of the N.
It had to be said.