"Inky pinky" appears in children's rhymes in the 19th century.

At least one pre-1914 version of "The Derby Ram" contains "hinky dinky" in the chorus.

In the U.S. for many years before the war, "hinky-dinky" meant contemptably small or inconsequential.

So I don't think these words stand for any particular French words in the song (though "Dis-donc!" "Hey, you!" might have called "hinky-dinky" to somebody's mind).