Charlie Chaplin is actually singing to the tune of "Je cherche après Titine" (I'm looking for Titine), a song by Frenchman Léo Daniderff (lyrics by M. Bertal, B. Maubon and Henri Lemonnier) and first released in 1917. Titine is the diminutive of some feminine first names like Martine and Clémentine. The lyrics are nonsensical but appear to have words from French and Italian. It wouldn't be the first time he uses foreign gibberish, however- he would fake German in "The Dictator" a few years later.

The Université de Napierville has a wonderful collection of French songs from 1870 to 1945 and provided me with the following:

In 1917, shortly before the First World War ended, the French soliders in the trenches were known to have sung to the tunes of La Madelon, another famous pre-war song. For the "sammies", the American soldiers in Europe at the time, the song was harder to remember, but it turns out that Titine, for some reason or another, was easier to recall. Hence, after having whistled it, sung it, played it on the harmonica, on the guitar or on the piano, they brought it back with them to the United States. While the story of the song could have ended then and there, it became a popular symbol of the end-of-war Paris and the 20s, and it became a hallmark of the era when Charlie Chaplin immortalized it in his first talkie film.

Download Charlie Chaplin's rendition in mp3 format