Indeed, even if you were to consider the Quebecois as a distinct subculture, a non-white Francophone is more a member of that culture than a white Anglophone.

Not a sociologist or an anthropologist, but a culture is composed of various cultural trappings, which include customs around food, dress, and language. There's not really a lot of room for a meaningfully defined Canadian culture that somehow excludes people with the wrong shade of skin colour. Butter tarts, Nanaimo bars, the Canadian "Sorry", much of what could be considered Canadian cultural trappings aren't that race based. Except maybe for Residential schools, but some things are better left in the past.