The "Caramagnole" and "Ça Ira" were out of favour under the Empire, "Velon(?) au Salute de L'Empire" was in.

You could try "Le Chant du Depart" a favourite with the 'Army of Italy' but likely to have made the transfer to sea, it's a good marching tune (remember marching pace is 80 paces/min, same as the Foreign Legion these days).
There are some more early (Army) songs which may have crossed over, one about piercing the flank and another who's chorus seems to revolve around 'I like onions fried in oil' ("J'aime l'oignons frits en huile" ? - I'm sorry, I know some bits phonetically, but I neither speak nor write French.

Any use?

Walrus