He is a purebred Canadien horse, chances are he's registered as plain old bay, brown, or black. Not likely as chestnut because both his parents were black. I wish I had a full body picture of him for comparison, but I don't.
I'm having this issue with my Paint filly. Her head is black, but her flank patches look COMPLETELY "bay" in color (a burnished mahogany color). They never look black. But both her parents were supposedly black, so it's the only possible color outside of chestnut. Or maybe brown, I don't fully understand how brown works, I know it's a type of agouti, so I'm assuming you actually NEED a brown horse to produce one or it would display physically.
I think it's safe to say that regardless, the OP's horse IS a red base. The question is just between him being a liver chestnut or a sooty palomino.