Tessier Family Genealogy Forum
I have a Gilles BADAILLAC who married Marie-Madeleine Therese TESSIER (b. 1705 in Repentigny) m. 26 Apr 1731 at L'Assomption. Could this be your couple? If so, he was the son of Gilles and Francoise GIGUERE. She was the daughter of Ignace and Marguerite LUSSIER. (This would make her the granddaughter of Urbain and Marie ARCHAMBAULT.) Not every file lists her as their child, but PRDH does.
They did have a son named Alexis who was christened at St-Michel, Yamaska, Quebec on 7 Apr 1740. Some records showed him deceased as an infant on 29 Jul 1740, but that's unconfirmed.
The only real way to find hard copies wold be to contact the Archives of the Archdiocese of St. Louis, Missouri or the Pearson Museum in Springfield, Illinois. They would have the only original records of the Northwest Territory. Since this was over 50 years before Illinois applied for statehood, there wouldn't even be an accurate census. The area was so rural that the priests would just travel up and down the Mississippi River in a circuit. so until the parish was set up, these towns were treated as missionary churches and would have had their home parish at St. Louis or Cape Girardeau.
Hope this helps. Let us know if it's not and we'll keep looking.