The war pretty much spelled the very definant end to american ambitions in canada, sure we won the lousina territory and some islands, that helped but it cut off a pontentially useful path to wealth. That said the French/Haitian invasion of DC was one of the big factors that convinced Virginia to end slavery, we almost lost the capital to an army of former slaves and that convinced a whole lot of fence sitters that slavery was too dangerous to keep around.
Maryland, and other boarderstates followed suit, the deeper south responded by doubling down on the insistution which would end up causing the civil war.
Speaking of that the civil war probally doesn't happen, it was only with the almost complete disaster caused by the french invasion where militias humilated themselves that caused america to fix their milatary. With out that fix and organization america doesn't defeat mexico in the mexican american war, and we don't seize mexican territory. With out the new territory being closed off to slavery in the new territories the deep south doesn't rebel.
And 3 brutal years of doomed fighting doesn't happen, this also butterflies the Lincon presidency, which butterflies the Lee presidency.