Has YVR-LHR already been flown? You haven’t posted other useful details so others can’t help. Have you looked at Air Transat? They have seasonal service to Paris but don’t know if they’re flying on your dates, but they won’t show up in most (any?) booking sites.

when you say AC is the best option, is that the best option they presented? What about OneWorld or SkyTeam? Did you check flying with BA via LHR? At that price I’m shocked you can’t find faster routings than via YUL, but you haven’t posted details so we can’t help.