There is no particular reason to think that the British would take control of upper-Louisiana. The British hadn't even tried to take New Orleans in any of their wars with the Bourbon Powers. New Orleans has natural defenses from a naval based attack as shown in the War of 1812. The population of Canada west of the Great Lakes was tiny until well into the second half of the 19th Century so there wasn't any land hungry hoard ready to pour over the border into the region. The British had little reason to have their small peace time army try to force the powerful tribes of the Northern Plains off their land to make way for a trickly of settlers. The native tribes could well hold their lands into the 20th Century.
Well, firstly, the 19th century was the period when social darwinist ideas reached their peak. Great powers were expected to be continually expanding, and anybody who didn't risked being left behind and eventually crushed by their more expansionist rivals, so I don't think it's really in keeping with the spirit of the times to leave large tracts of prime agricultural land empty. And the native tribes really weren't all that powerful -- the US was able to make do with an army of around 16,000 strong to cover its entire western frontier. If Britain, or France, wants to settle more land in North America, the natives aren't going to post much of an obstacle.
Secondly, a lot of the capital to fund US industrialisation can from foreign (read: British) investment. Without a unified US powering across the continent, some of this money would doubtless be spent on other things, but some would be spent on investment anyway -- in the balkanised US states, in Canada, in Britain itself, in some other part of the Empire. So even if the North American continent as a whole is less industrialised, the Allies might be able to make use of more industrial capacity from elsewhere compared to IOTL. Particularly given that the US, whilst it was pro-Allies from the beginning, wasn't an active participant for most of the war, and didn't put its economy on a war footing until 1917. If investment that went to the US IOTL goes to Canada ITTL, then not only will Canada have more industrial capacity, but this extra capacity will be directed towards the war effort from the beginning.
