While I am not sure of any connections before 1860, at the time of your Joseph Beauvais I would be looking for an Albert Beauvais married to an Amslie Lamakie. I do not have dates, but these were the parents of my great-grandfather Austin (Augustin) Beauvais. There is a belief of a Mohawk connection with my great-grandmother Alphonsine, but I have no information. It seems as if there are many brick walls with the Beauvais connection to the Malone area. Perhaps we have some names in common. If I can be of help somehow, let me know. I'm very willing to share what little I have on this line.