Think about it. What if Napoleon saw the strategic benefit of making an official alliance with the United States entrenched in a war with a common enemy (Britain) during the War of 1812. Perhaps then could've sent arms, supplies and maybe even troops across the Atlantic allowing the US to make gains in British North America and potentially turning the tables on the war with the US emerging as a world power early on in the Ninteenth Century using resources found in the captured Canadian lands.