The anonymous guest at 1:24 was me.
In Chants de marins, à la découverte d'une tradition vivante, Michel Colleu/Nathalie Couilloud, Ed. Chasse-Marée, they say that the song was published as early as 1845 in La France maritime and was later collected many times near seamen from Brittany, Normandy and Vendée -I doubt that all those seamen knew how to read. They too say that the song was probably written around 1810 and that a version collected in 1985 sung by a fisherman from Fécamp who used to fish off Newfoundland gave some hints: it said that a fregate left St Malo to go fight the English on their 100 canon vessel and returned to St Malo, which would refer to the fight mentioned above.
I agree that "A la santé du Roi de France" is more fun, beside "Hourrah pour le Premier Consul Bonaparte" wouldn't have fit the tune!