I don't know anything about the English version. Below this YouTube there's some info that translates as... "Passant par Paris" is a song probably dating from the sailing navy, and which has had several versions. However, it is best known for being "imported" by said sailors in Paris, where they fought valiantly in 1870, under the command of La Ronciere le Noury. Their colleagues from the Troupes de Marine (Navy troops) also had their big moments at Bazeilles, Fort Montrouge (first image) ... This explains the images of the siege of Paris, the war of 1870-1871 and the navy of Napoleon III." (thanks Google translator!)
Here it reads that it's an old sea chanty from before the Revolution (= before 1789) but I could find no reliable document.