Something to consider- the US had strong trade ties to the Ottoman Empire (I'm refering to it as Turkey) during this time, there's a reason US ships were getting seized by the Barbary states in North Africa... because US ships were there in large numbers. A lot is written about the triangle trade with Europe and Africa because of the slave trade and its impact on US history, but at the time the more important triangle actually was the US-Turkey-China triangle. The US had official relations since 1780 with Turkey and it was a big source of opium to sell to China, the USA having nothing else at the time to sell the Chinese. Later on in OTL President Monroe would make a speech declaring that the USA would not support the Greeks against the Turks and not get involved in European affairs... but it has come down to us for the less important at the time part- the Monroe Doctrine that Europe would not be allowed to interfere in the Americas.
A Napoleon occupied and therefore extinct Turkey would affect the US economy if Napoleon didn't allow US shipping to and from Turkey. We could see War of 1812 butterflied away and instead a more intense and longer Quasi War. If no Turkey, and Greece is nominally independent under French tutelage, there is less reason for Monroe to make his speech, less reason to throw in the Monroe Doctrine (which was empty and was simply piggybacking on already established British policy that OTHER European powers were not to interfere with the newly independent nations in the Americas or set up spheres, because British policy was open door and free trade).