As Marc points out, Napoleon not squandering a sizable army in Haiti (although it was certainly producing a lot more revenue from sugar than New Orleans and Louisiana Territory were yet) is probably the POD, putting far more troops under competent command several thousand miles downriver from English Canada, enough to conquer Canada from West to East or at least draw what Canadian/British troops were available to defense.
That'd make the U.S. war even more of a minor sideshow to the British than it was while eliminating the penultimate battle of New Orleans that salved American pride and put Andrew Jackson eventually in the White House...so lots of significant repercussions here.
Whether the U.S. would have invaded Canada and burned down their capitol, resulting in the burning of the U.S. White House, Library of Congress, etc. gets much less uncertain (would the U.S. mount a bigger and more successful invasion of Canada's East Coast in coordination with the French coming up from the West in 1814 (that's several thousand miles up river and big logistics, sending large raiding parties with mostly local Indian auxiliaries would be more likely both as an old French tactic here and the British tactic in Louisiana Territory during the War of 1812.
France retaining the Mississippi, Missouri, and most of the Ohio river valleys as the hamlets that were becoming Chicago and Detroit as well as St. Louis and New Orleans would be a lot more interesting after some years of the French Army learning the region's possibilities like rich farmland, hardwood forests, lead, sulphur, and some of the world's best and biggest iron ore and copper deposits that'd make the region look more like New France and less like a backwater best sold to the Americans.
French alliance with the Americans is hardly far-fetched although President Monroe was upset with French behavior towards U.S. ships and crews at the same time, and it had only been a generation since the previous French alliance and intervention here. U.S. privateers doing even more damage to Britain's highly profitable trade and taxbase in Bermuda, Jamaica, Trinidad, etc. would be likely with French encouragement and maybe naval cannons.