By demise of "its ally" are you referring to the defeat of Napoleon in 1814 or Napoleon seizing control?

You may be overestimating how much Napoleon cared about America. America really was regarded as a small and relatively unimportant country at the time, particularly by France and Britain who were locked in a continental existential conflict.

Napoleon ignored and refused to meet the majority of American ambassadors and messengers sent to Europe, even when America foolishly went to war with Britain he only hoped that they would stay angry enough to distract the British and offered no help, he didn't even have the resources to. Napoleon was cash-strapped and even urged the capture of American merchant ships throughout his rule.

The British thought that Napoleon was helping or supporting the Americans in their war, it was the only explanation at the time as to why America started such an impossible fight. They even held back slightly on their blockades of American ports as Admiral Warren (chief of the North American station) was worried about an inevitable French fleet turning up - it never did, and never was going to.

The French did like the Americans distracting Britain, and when the beleaguered US administration mentioned an early, embarrassing peace offer, the French ambassador in Washington urged Paris to let the American ambassador Joel Barlow travel north to Napoleon's HQ Vilna with a trade treaty (he would never sign). He never met Napoleon who went past him without caring and Barlow died shortly after. There was no communication between the two nations for months after that.

At one point Napoleon allowed the American privateers to use their ports, but the US was unable to offer the same as the administration didn'd have enough support to change their law about helping foreign privateers, and even more embarrassingly couldn't even stop US grain merchants from supplying (the essential, at that time irreplaceable) grain to Wellington on Spain. They were literally supporting Britain's best general fighting against their own "ally".

America had no naval strength, no 'blue water navy', a weak government who lost essential support when they forced the country into an unwinnable war, no money and nothing to offer the French. They made no impact on British sea power and most importantly had no effect on British maritime trade - the only thing they could have used to force Britain to come to terms. Some people may say that the American privateers - the Republican's "private navy" - were successful, and individual ships may have been, but the steady recorded insurance rates of Loyd's of London is the clearest indication that British shipping was never under threat.

Edit: the American reaction to a fallen Napoleon

With Napoleon in retreat Britain replaced the grain they needed from America with that from other countries in Europe as trade re-opened. The Canadian frontier was pretty safe and America was bottled up, with no ability to get to sea and Britain still had complete control of the Atlantic. The British blockades had bankrupted the US, they had nothing to barter with. Their original war aims, the end of impressment and the occupation of Canada, were completely ignored when Britain and America finally came to peace. America got lucky with the terms as Britain was more engrossed in sorting out Europe after Napoleon, but they had been beaten and chastised. It's no coincidence that they turned inwards, expanding across the west and down to Mexico after such a disastrous first attempt at standing up to the big dogs at sea.