Here's some interesting information on the background of the song:
This song has been well known as a children's song in Creole Louisiana since the nineteenth century. It comes from a song sung by enslaved people and has a distinctly Caribbean feeling. ...
It is not at all uncommon that songs of enslaved people turn out to be coded messages. Scratch the surface and you find deeper meaning. In a 1925 manuscript, Ruth Harrison discusses what is clearly an early version of Monsieur Banjo in which the banjo itself becomes complicit in a discussion of the politics of color and class in the city. Harrison says, “When the negro sang, and had something to say of a confidential nature, he always addressed a banjo, real or imaginary, as if it were some comfort to be certain of an unprotesting and ... sympathetic audience." This version of the song begins; "“Getee’ ce mu-le la ‘tit banjo", or "Look at that mulatto there, my Banjo" and protests that this proud banjo denies the singer to be his cousin.