I have a theory about the Jean Marie thing. I have the birth records for both Jean Marie and Antoine. They were both born in Entre-deux-Guiers, Isère (south side of Le Guier River) while the other three children were born in Les Échelles, Savoie (north side of the river). Jean Marie was born in 1879 and Antoine in 1882 - they were definitely two separate people.
The first census both could show up in was the 1886 but only Jean Marie is there BUT his ages makes him born in 1882 not 1879. This continues on until the 1906 census by which time his father had died (he was in the 1901 census). Now it shows Antoine with an 1882 birth year, living with his mother.
I think Jean Marie died either in infancy or as a young child, probably close to when Antoine was born. I haven't been able to find a death record. I think Antoine's dad, for whatever reason, started calling Antoine Jean Marie, because it's as soon as his dad had died that he is able to call himself Antoine. I would certainly understand if that caused Antoine some major issues with his dad.
The other hint for this theory is that in the 1901 census Jean Marie is living with his parents and is employed as a locksmith. In the 1906 census Antoine is a lathe operator which advanced locksmiths usually were.
There's usually some truth in family rumours. Sometimes they provide wonderful clues. I had one friend who's dad claimed his great-great grandfather came over from France and married an "Indian Princess" but most of the family said it was just a pipe dream and laughed about it. I recently "found" her and discovered not only was it true, she and her French husband were extremely important in the local history, there are plaques in their memory and citing their accomplishments, and she was Tecumseh's cousin. They aren't laughing anymore - lol.