You might try Histoire de la chanson populaire en France (1889) at Google Books. Although it may not provide the songs themselves, it should give you some titles to investigate. It does contain the melodies for a number of songs.

Also:
Chansons populaires du pays de France (1909)

Here's an entire web site of French sea songs: Chansons des marins
Some of the songs come with MP3s. Sadly, historical info looks scarce.

I believe Stan Hugill gave a number of French sea songs in his books, along with their history. But as I got the books from the library, I can't easily check which ones might suit.

Haven't checked on dates, but "(Il était) un petit navire" may be a possibility, since it gave rise to some British and American sea songs, like Thackeray's "Little Billee". Hunting up an interesting tune for it may be a challenge, though, as I recall from my earlier efforts.

Check out Les Cap-Horniers. A listing of their repertoire may be found here, with brief descriptive notes.