My efforts to pin down where Joseph Deraque might have some from are thwarted by the realization that “Deraque” isn’t an actual last name. So, the question is what kind of name is “Deraque” the messed up version of? If we search for Anthony Fagot–remember, he’s Joseph’s boss–the only historical reference I could find to him, other than in Arkansas, was as a merchant in Ste. Genevieve. The “St. Louis” clue is, as of yet, right now, unconfirmed.
So, I couldn’t find any names even vaguely like “Deraque” in any other French cities. But, there in Ste. Genevieve, in the early records I could find, there are Durands, Durochers, and Girards. Durand and Girard are both names “Deraque” has been Anglicanized to, which makes them possible cousins of Joseph. But I also found a really interesting footnote that I’d like to confirm, should I figure out who to ask, that the “illiterate” French folks along the Mississippi had a habit of pronouncing things oddly. So, some people said “Prairie du Rocher” like “Prairie du Roe-she” but with equal stress on both syllables and other said “Prairie du Rock-eh,” with, as far as I can tell, almost no stress on the “eh.” How close to “Deraque” might “Du Rock-eh” come?
Anyway, Ste. Genevieve is the best lead I think there is.