"curtisports2" is completely wrong. The U.S., either naively or arrogantly, hoped to have unrestricted trade with France which, during Napoleon's reign, was the aggressor of Europe. France always had a coalition of other European powers allied against it. The U.S. could have limited its trade to all countries BUT France. In that way, it would have still done as much business. It also would not be regarded as an at least tacit ally of the aggressor. There was no need for Madison's folly, the war.
Note that, after the 1763 Treaty of Paris that ended the Seven Years War, there was no "French Canada." "Nouvelle France" had all been ceded to the U.K. in that treaty.
The U.K. had no war aims whatsoever in N. America in those years. When Madison declared the war, it did the minimum necessary to stifle U.S. imperialism. It was far too involved in Europe, & had no wish to expend resources elsewhere.
When Napoleon was defeated in April 1814, the R.N. no longer stopped U.S. ships sailing to France & didn't impress sailors. The primary casus belli for Madison dissipated. In August, the U.K. sent a small portion of Wellington's Peninsular Army to the U.S., where it routed a much larger U.S. force at Bladensburg before putting much of Washington D.C. to the torch (saved by a timely heavy rain). That same month, peace talks were begun at Ghent (then the United Netherlands, now Belgium).
The U.S. was in deep financial straits, & wouldn't have been able to afford an 1815 campaign. U.S. diplomats, led by J.Q. Adams, decided not to present Madison's mad demands for an end to impressment & suggestion that the U.K. turn over Canada to the U.S. Finally, on 24 Dec. 1814, the Treaty of Ghent ended the war. None of the U.S. war aims had been met. The U.K. desire to end the war was met. 100% of Canada's war aims were met. It was, no matter you choose to look at it, a major defeat for the U.S., which was in dire economic shape due to the war. This lasted into the late 1830's.