The term Papaout has nothing to do with Stromae’s song, Papaoutai (where are you, dad?) that reached number one on the music charts of several Francophone countries between 2013 and 2014.
Papaout and the verb Papaouter appear in an early 20th Century Parisian slang dictionary as synonyms for pederast and the practice of pederasty (that is being top homosexual man or sodomizing someone) and, subsequently and to this day, we can find the expression Empapaouter which means to sodomize or fuck the ass of someone in its most literal sense.
The origin of this expression is not clear and, as usual, we can find several explanations. The first and more popular relates to the expression Va te faire voir chez les Papous! (Go to be visited by the Papuans!), that would lead to Va te faire enculer chez les Papous! (Go to the Papuans to get your ass fucked!), a meaning and a phrase construction we also see in the expression Aller faire voir chez (ou par) les Grecs! (Go to be visited by the Greeks!), where the relationship with homosexuality may seem more obvious. But if we can picture ourselves at the time, and taking into account the exotic and “barbaric” customs of some tribes of New Guinea as the Etoros and Sambians, the relationship is much clearer.
The second explanation refers to the etymology and the somewhat older use of the Empaouter and Empapaouter verb, around the year 1900. They were used in a somewhat ambiguous way as synonymous with annoy, get shitty or get dirty. Here the relationship lies in the social vision of homosexual anal intercourse: there is nothing more annoying and dirty than letting your ass be fucked. Pulling the thread of this explanation we find the term Papote, which in ancient French was porridge or mush, and hence, to be covered in porridge or mush, as synonymous to have gotten dirty, muddy or shitty.