The Wii U does not natively support GCN games or have a GCN mode. Are you talking about Nintendont perhaps or do you mean just vWii mode after all?
The Wii Remote should work in vWii mode. Is it a genuine one? Does it have Wii Motion? For Nintendont, the Wii Remote will work but does require a Wii Pro/Classic controller Add-on.
Alternatively, the USB Wii/Wii U/Switch/PC -> GCN adapters do work quite well if you have a GCN controller.