He is perhaps best known as the author of "Non, je ne regrette rien" ("No, I regret nothing"), written in 1956, with its most notable recording completed in 1960 by singer Edith Piaf.
Dumont tells in the book Édith Piaf, Opinions publiques, by Bernard Marchois (TF1 Editions 1995), that Vaucaire's original title was "Non, je ne trouverai rien" (No, I will not find anything) and that the song was meant for the popular French singer Rosalie Dubois.
According to journalist Jean Noli, in his book Édith (Éditions Stock 1973), when Dumont and Vaucaire visited Piaf's home at Boulevard Lannes in Paris on 24 October 1960, she received them in a very impolite and unfriendly manner.
At the time of the recording, France was engaged in a military conflict, the Algerian War (1954–1962), and the 1st Foreign Parachute Regiment—which backed the failed 1961 putsch against president Charles de Gaulle and the civilian leadership of Algeria—adopted the song when their resistance was broken.
The leadership of the Regiment was arrested and tried but the non-commissioned officers, corporals and Legionnaires were assigned to other Foreign Legion formations.
They left the barracks singing the song, which has now become part of the French Foreign Legion heritage and is sung when they are on parade.
Vaucaire and Dumont wrote a song about the Berlin Wall, which had just gone up, called Le mur, intended for Piaf.