You seem to be building up a very interesting picture here.
Correct me if I get any of this wrong.There's Thomas and son Solomon, both of them navigateurs, in French-speaking Canada in the 1780s.Though their names don't sound French, Solomon marries a woman with a French -sounding name in Quebec in 1781, so apparently the family at least has French associations.
A man who looks like Solomon's son Augustus turns up in RI, then in Pa (1850) and then in New Orleans (1860).
Although I know little about the Acadians, some online information seems to confirm that all of these locations were places of Acadian migration.Could Solomon's wife Marie, or even Solomon himself, have been an Acadian?There's a Rootsweb list Acadian-Cajun-L.It might be worth posting an enquiry there.Two links I found (but haven't read):
Also- since Augustus was a screwman, it might be worth exploring records of the Screwmen's Benevolent Association of New Orleans to see if he was a member.There might be additional information about the family.