Why Did Charles and Mary Mathieu Move Back to Canada?
According to his Ontario birth certificate, my great-uncle Jean Charles Horace Mathieu was born to Charles Mathieu and Mary Agnes Proulx in Fort William, Ontario on April 24, 1911.
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. 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). 
My great aunt told me that most of the family, except for Raymond, moved back to Canada from Michigan after his dad lost his job in the depression.
I wasn’t able to find them on the 1930 U.S. Census, so if they did go to the States and returned, the entire experience probably happened between 1921 and 1930. 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.
They were back in Montreal by August 8, 1940, when Jean Charles volunteered for the Royal Canadian Air Force.
To find out their address, I used Steve Morse’s search engine at Steve Morse’s website to search Lovells directories. I found carpenters named Charles Mathieu living at 6760 St. Denis in 1932, and at 3286 St. Antoine in 1940. There were no listings for carpenters of that name from 1933 until 1939. Also, I don’t have anything to say whether these listings actually represent Charlie’s family.
My original question remains a brick wall.
 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.