Possibly....at the moment, Canada seems to be a gigantic version of Northern Ireland during the troubles....between the descendents of the Patriots and Loyalists in this world.
In any case, the USA keeps New Caledonia (you think they'd have renamed British Columbia, right?)
I'm not sure if they would have renamed BC or not. If they did, they would not trade one British name for another. It would be Columbia Nova most likely IMO.