Don't believe so. During this period, American and French and British relations were pretty rocky all way 'round... mutual distrust, trade disruptions, infringements and embargoes, to the point of open naval battles between all three. Though war was not formally declared on France by America during this time, it was seriously considered. When the French entered into war with the English, America did not become an ally to France in the conflict, instead, saw an opportunity for retribution for British naval disruptions and to further expand American territory while British forces were occupied in Europe. The War of 1812 in North America was to a large extent an isolated event, separate from the Napoleonic Wars, until Napoleon was defeated in 1814, and British forces were freed up in Europe and able to turn their full attention toward the Americas again.
Check out American French relations after the Revolutionary War. To sum it up, America distrusted and resented the English and the French... just distrusted and resented the English more.