The French surnames ended up being spelled many ways after the people immigrated to the U.S. Snay, at times, is a variant of Senet, Senez, Sene, et. I checked through marriage records in Quebec. I found this possibility for you:
Marriage:On April 13, 1807in Saint-JacquesTown/District:Saint-Jacques/Montcalm, Qc Louis Payer-PayetteSon of [ Joseph Payer-Payette & Josephte Lacourse ] and Louise SenetDaughter of [ Joseph Senet & Marie Cadorette ]
In Louis' Father's marriage record, the surname is Paille. The surname of Lacourse was a dit [aka] for the surname of Gelinas.
Marriage:On November 25, 1772in Sainte-AnneTown/District:Yamachiche/Maskinonge, Qc Joseph PailleSon of [ Joseph Paille & Josette Gerlais ] and Marie GelinasDaughter of [ Jean-Baptiste Gelinas & M.-Josephte Lacerte ]