I'm curious to know what information you have that leads you to believe that William is Joseph's son. Let me tell you what information I have on these two people which also makes me think that William is the son of Joseph (Joseph is my great-great-great-grandfather).
In the St-Anicet church records, I found a baptism (June 25, 1864) for Marie Rivet, daughter of William Rivet & Sophie Beauvais from Riviere-a-la-truite. The godfather is Joseph Rivet and the godmother is Josephte Lajoie (his second wife). My assumption is that Joseph & Josephte are the child's grand-parents (in fact Josephte would be William's stepmother).
On June 24 1839, Joseph married Madeleine Barrette in Hinchinbrook. I have 8 children for this couple. I was able to find the birth dates for only 3 of them (André, Virginie #1 &Virginie #2). Another three showed up on marriage records as being the son/daughter of Joseph & Madeleine (Joachim, Emilie & Jacques). Then there's William who I am currently showing as a child of Joseph & Madeleine based on the above assumption. The 8th child is my great-great-grandfather Pierre. I'm relying on the Drouin Institute's information to link Pierre to Joseph & Madeleine but I have yet found the proof that links them without any doubts. Madeleine died on January 20 1849. On Aug 27 of the same year, Joseph married Josephte Lajoie in St-Anicet.
This doesn't give you the exact information you are looking for but hopefully it will help solve the mystery. Let me know if you have any other information for William or Joseph.