Marcello Mastroianni did not dub his own part. This is not his voice.
In its original version, most of the French speaking characters were obviously dubbed by moderately not convincing Italian actors.
The cabaret where Eartha Kitt sang "Babalu" was called "Le Perroquet Club" and it was the one where she sang "C'est si bon" for the first time in her career at its opening on November 4, 1950. Rita Hayworth and her husband Prince Aly Khan were present.