In the 1600's there were apparently a lot of Indian raids in New Hampshire. Many NH residents were killed, some were taken captive and taken to Canada. Some returned to New Hampshire, some stayed in Canada. I only know this because I, too, am searching Shaws in Quebec. My Shaw moved from Quebec back to New Hampshire and I've always wondered if it had to do with the fact that the family was originally from New Hampshire at the time of the Indian raids.
My great grandfather was Christopher S. Shaw, born 3/20/1842 in St. Martine, Quebec. He moved to Dover/Strafford NH. He first married Clara D. Robinson, who was born 7/12/1855 in Deerfield, NH but she died of TB at age 17. He next married Sarah Jane Foss, who was born 3/7/1857 in Strafford, NH.
The son of Christopher S. Shaw and Sarah Jane Foss was Wyman Robinson Shaw, born 2/4/1891 in Strafford, NH. Wyman was my grandfather.
I have pictures of Christopher. He was a stocky, but not fat guy, with white hair and a bushy mustache. Early on in my genealogy days when I didn't know enough to record sources, I noted that Christopher's parents were John Louis Shaw and Marie Dirrais, but I have never verified this and don't even know where it came from.
If you make any progress on Shaw's in Quebec, I'd love to hear from you.
Susan Shaw Phillips