Ooo... If Napoleon only sells New Orleans, then Britain might 'encourage' Canadian forces to move west, building some infrastructure (such as ship yards) on the Great Lakes, and move into the Upper Louisiana territory. Note, for instance, that Astor hasn't set up his furtrading operation at Duluth yet, and the only white presence is the Northwest Company.
Heck, even Fort Dearborn (on the site of OTL Chicago) wasn't founded by the Americans until 1803.
It would be fairly trivial for the Brits to take control of OTL Wisconsin, say, since it was still under British control until the War of 1812 (even if it was legally ceded to the US with Independence).
IF, then a War of 1812 equivalent happens, there would be an existing infrastructure on the Lakes far in advance of OTL (well, meaning any at all), Britain could KEEP control of the Lakes (instead of the US managing to do so), and the US would get curbstomped in the West.
End result of THAT would be Michigan (possibly), Wisconsin and northern Illinois being British, and the border being, say, 40N instead of 49N.