I'd say that Edith was French both by nationality and culture. She didn't consider herself an immigrant. I was under the impression that her father was at least neutralized or born in France (which doesn't give automatic citizenship like in the US) if not actually French, but her mother was foreign. Either way, regardless of what French society at that time thought, Edith considered herself French. That doesn't mean that it couldn't have been meant in that sense and it's a valid option. I don't really see it applying to Edith, but Edith didn't write this song.

I personally always took "girl of the harbor" to mean "prostitute", especially when keeping Edith's background in mind. She herself translated as "girl of the harbor" on Sullivan but the Americans wouldn't have let her say "prostitute" on national television anyway. Whether that was what was intended, that's what I'll always think.