I think Napoleon likely would have allied with the US over the long term. The US did not have the baggage of nobility, was ruled by enlightenment thinkers, and we already had a common enemy in the British.

That said, the US was a sparsely-populated backwater outpost at the time with only about 7 million inhabitants (a million of whom were slaves). For comparison, the population of Europe during the same time was close to 140 million. We simply didn't have the manpower, infrastructure or money to meaningfully contribute to a European conflict at the time.

That would have never happened without British involvement, since they controlled the sea. Furthermore, as the article pointed out, Napoleon and America shared similar ideals. Finally, fighting a war in your homeland is infinitely easier than the supply lines Napoleon would have had to maintain to fight in America. It would have been absurdly expensive and would have opened France up to attack from its unfriendly neighbors. In conclusion, I do not think there is a likely scenario that envisions an America under Napoleonic rule.

Napoleon sold Louisiana to the United States of America, so most likely he didn't care too much about this region. Granted, he may have been afraid of not being able to maintain it because of a naval inferiority, but I don't think expending in America was amongst his priorities.

Considering that America and France both shared a common enemy - Britain - during that time, that would be highly unlikely. The Louisiana Purchase also made that prospect unlikely, as did Napoleon's explicit admiration of American ideals and leadership (as the article pointed out).

What reason would Napoleon have to attempt (and probably fail; the American navy was not nearly as much of a pushover as you state the army to have been) to launch a trans-Atlantic campaign against what was historically an ally and a strong cultural/political influence?