I’ve been trying to trace my great-uncles’ family ever since my great aunt told me that everyone, except his older brother Raymond, moved back from Michigan after Charlie’s dad lost his job in the depression.
According to his Ontario birth certificate, my great-uncle Jean Charles Horace Mathieu was born to Charles Mathieu and Mary in Fort William, Ontario on April 24, 1911, so that’s where my research began.
Ten years later, the family had moved to 500 Aylmer Avenue in Windsor, Ontario, where they were renting a six-bedroom house. Both parents were 51 years old by then. His father Charles worked as a carpenter. His wife, who was born Marie Agnès Proulx, was then called Agnes. (She went by Mary and/or Agnes depending on the documents.)
Jean Charles had two older brothers, Arthur (16) and Raymond (14), an older sister Fernanda (12) and two younger brothers, Lawrence (8) and George Albert (6). 
There’s no hint of the family from then until 1932. There is one person who has a family tree on Ancestry who indicates that a Fernanda Mathieu crossed into Canada in 1924. That may have been John Charles’ sister, but it isn’t confirmed.
I wasn’t able to find the family on the 1930 U.S. Census.
By using Steve Morse’s search engine to search Lovells directory, I was able to find a carpenter named Charles Mathieu living at 6760 St. Denis in 1932. I don’t know whether this was Charlies’ family or not.
If it was, they left Montreal again, because there are no listings for carpenters named Mathieu between 1933 and 1939.
Their next appearance in Lovells is 1940 when a carpenter named Mathieu lived at 3286 St. Antoine.
That’s definitely them. I have an undated newspaper clipping about Aircraftman J.C.H. Mathieu between injured in a flying accident that says his parents lived at 3286 St. Antoine.  That clipping is undated, but I know that Jean Charles Mathieu lived in Montreal when he volunteered for the Royal Canadian Air Force in Montreal on August 8, 1940.
My original question remains unanswered.
 Photocopy of Province of Ontario pocket birth certificate issued at Toronto on November 10, 1947, registered in April 24, 1911 in Fort William, Thunder Bay District by Geo. H Dunbar, Registrar Dunbar.
 1921 Canadian Census, Province of Ontario, District of Essex North, Roger West Minard Subdistrict, Number 47, June 13, 1921, B, Page 20, derivative source.
 Lovvell’s Montreal Alphabetical Directory, 1932, p1456
 Lovell’s Montreal Alphabetical Directory, 1940, p1771.
 “Airman Injured,” Montreal Gazette, undated clipping, author’s collection.