Easiest way is to avert the Louisiana Purchase, or to have Britain conquer it in 1812. This cuts off the USA from the west, which is obviously going to have huge ramifications. After that, have your favorite north-secedes scenario (probably during the war of 1812) or south-secedes scenario (ACW analogue.) If the former, you can probably take chunks of the old northwest in, given how the British badly wanted control of the Great Lakes as well.
Here's an idea I just had:
The PoD is during the French Revolution. Just after the Tennis Court Oath is taken, a compromise is worked out between the National Assembly and the remainder of the Estates-General. The monarchy will remain in power but will be reduced to all but a figurehead role. The Estates-General is replaced with a bicameral system similar to the British Parliament, with the First and Second Estates being combined into the upper house, the Senate, while the lower house, the National Assembly, will be drawn from the Third Estate and popularly elected. While a radical faction of the National Assembly attempts to storm the Bastille, they are massacred by the military.
As a means of dealing with the overpopulation of France, the French government encourages large numbers of people, with offers of free land, to move to the Louisiana Territory. This massive increase in settlement leads to Louisiana being considered an important part of the French Empire, if not an extremely profitable part.
Meanwhile, in the United States, the Federalists have continued to dominate the political system, and have moved towards an increasingly one-party state, as the Alien and Sedition Acts result in the suppression of political opposition by the party.
Eventually, a war will break out between France and the United States, under the pro-British Federalist government of John Quincy Adams. This war will result in the defeat of the main American army under the leadership of General Andrew Jackson at the Battle of New Orleans. The Federalist regime collapses under popular revolt, with an unstable "popular government" coming to power. This government will be eventually replaced by the military dictatorship of Andrew Jackson after the economy collapses due to a massive unpaid war debt.
Jackson's dictatorship stabilizes the country in the short term, but strangles the life out of the country in the long term. The Jackson dictatorship continues the worst of the Federalists' authoritarian policies, but eliminate their economic policies and replace them with populism. The remnants of the Northeast elite, tired of Jacksonian rule after several years, will appeal to Britain for aid. The British, already on a collision course with the United States over border issues, will aid the Northern rebels, who will establish the Federal Republic of America, with its capital in Hartford, Connecticut.
By the mid 1800s, the United States will have been reduced to a shadow of its OTL self, with an authoritarian government dominated by slaveowners controlling OTL South and parts of the Midwest.