When America invaded British Canada in June 1812, Napoleon was taking the Grande Armee into Russia. Despite the Continental System and trans-European boycott of British trade, the British still had naval superiority and France couldn't really project policy in the Americas. After the Peninsular War, Britain sent some veterans from the now-allied Spain to America and they sacked Washington in August 1814 to avenge the sacking of York. The invasions of New York and Baltimore in the new year failed though, and the American-British conflict ended in status quo in February of 1815. Napoleon's biggest aid to America really was that he was a distraction.
During the French revolution, America protected several political refugees whom the republic wanted to execute, and refused to pay debts owned to the crown, once the crown was deposed. Tensions over maritime rights and other minor diplomatic faux-pas, plus Napoleon's later rather un-republican government and stylings, didn't help matters.