-The American southwest is part of Mexico. Like northern Mexico in OTL, it remained relatively underpopulated until around 1900, when population growth in the South lead to a lot of internal migration.
-Spain held onto Louisiana, Florida, and the Coastal parts of Alabama and Mississippi, called Spanish Florida. It became dependent on slavery like Cuba and the Southern U.S., and soon grew very wealthy off of it. In 1833 when a war in Spain broke out it took the opportunity to secede. It is richer than the rest of Latin America, but poorer than the other states of North America, its racial composition is similar to Cuba's.
-In OTL some French Huguenots established a settlement in Florida in 1562; they were later massacred by the Spanish. In TTL they tried again, settling New England in order to be a safe distance from the Spaniards, in hindsight, this is a much more hospitable climate to settle. Like in OTL New England, they grew rapidly after the first few years of acclimation, and were joined by more refugees as tensions flare up in France, at first the French government encouraged this, but later they sent Catholic rulers to the territory. This, along with anger over taxation led to a rebellion in 1660, establishing the Republic of French Florida. Boxed in by the French to the North and the Dutch to the West, French Florida did not expand, and so did not have the same "pioneering spirit" as other states and colonies of North America. It's population continued to grow until it was more densely populated than most of Europe, and there is little immigration from elsewhere. Like other Calvinist areas(Switzerland, the Netherlands, New England in OTL) it largely abandoned religion eventually and is today one of the most secular of the European-derived nations. Initially, it was largely an oligarchy, divided into "counties" with the governors of those counties, a position that is de-facto hereditary, sending representatives to a Governing Council. In 1819 a revolution occurred, replacing it with a democratic system of government. After initial border wars with France in 1687, and 1723-1732, New France largely avoided foreign entanglements.
-In Canada where Catholic French had settled before the revolt in French Florida, the French government endeavored to settle it with Catholic French, offering free land to Catholic migrants, Protestants were not allowed to enter. Like the Quebecois, their population grew rapidly, but was initially larger, with the result that the Quebecois are numerous enough to fill Ontario and the Great Lakes region, waring the with Dutch to the South, and meeting the Japanese in the West. In 1792 the French Revolution occurs and the radical leaders declare French Canada to be "self-ruling," however they interpreted it as a more symbolic gesture than the Canadians. In 1798, when the French government fired the Canadian born pro-revolution governor and sent someone from the metropole to replace him, he declared the colony independent. The French, busy with wars in Europe, do not put up much of a fight, but still claim the country until 1822. Canada becomes essentially a dictatorship under the rule of the governor-turned president, continuing through several dictator-presidents until 1873, when a limited-suffrage government is founded after a violent revolution. Universal male suffrage does not occur until 1905. Canadian opinion is broadly pro-French, and Canada quickly joins France's side in World War I and World War II.
-In the New Netherlands, the Dutch were successful in holding the colony, as the French in French Florida and Canada are busy fighting one another. It soon grows into a major economic center. The population here is the most diverse as OTL New Netherlands was, but eventually they fuse into a Dutch-speaking "American" identity. By the early 1700s there was major tension between the colonists and the Dutch appointed governors they replaced, however, there is no revolution, as the colonists do not want to fight the British to the South and the French to the North alone. But they get a chance once France invades the Netherlands. The new government is essentially a presidential dictatorship thereafter, with the successive presidents using the rivalry with Britain and Canada to silence opposition. The country expands to the West. In 1848 the revolutions in Europe spreads across the Atlantic, with the President making some reforms. in 1873 there is another revolution, soon followed by a dictatorship, which continues until a socialist revolution in 1911. Though the new government was not nearly as homicidal as the Soviet one, it severely mismanaged the economy. It was finally overthrown in 1935 following a war with the Japanese and democracy was restored. Socialism was democratic from then on, but still culturally and politically significant, like OTL France.
-The British established colonies much as in OTL in the American South, but they would be the only ones who remained British "colonies," eventually evolving into a Commonwealth Realm as Canada did in OTL, called Columbia. The colonists had conflicts with Britain about taxation and later about slavery but they did not secede in either case, owing to a desire to have British support in their rivalry with the Dutch to their North. Following a loss in a war with "America,"(i.e. Dutch America) in 1866 they agreed to a British plan for gradual, compensated emancipation. The British also have a colonies in Newfoundland and Nunavut, these are both governed as "crown dependencies."
-Rather than closing themselves off to the world the Japanese adopted Western ways and soon began to voyage to America to trade with the Spanish in Mexico. They established settlements on the coast of California and Oregon, though they are later driven out of the former by the Spanish. At first they were uninterested in colonizing North America, but soon trading posts evolved into colonies reinforced by refugees fleeing Japan's political conflicts. In 1678 these colonies seceded from Japan, whose rule over them had been nominal anyway. They soon expanded inland, eventually running into the Dutch and French. Their form of government was initially an Empire modeled after feudal Japan, but this was ill-suited to an area where peasants could simply move West. Wars are rampant throughout the country's history and it was often compared unfavorably with Japan, the latter seen as much more civilized. It was the last North American state to democratize, with the dictatorship overthrown in 1993.
-Russia establishes Alaska as in OTL and settles it in a similar manner and for similar reasons as it settles Siberia.
In each case the polity is more comparable to France or Germany, or a much smaller country, than to the United States. Britain is considered the world's strongest power, rivaling Russia. America(i.e. the former Dutch colony) is still noticeably more socialist than other American or European countries, while capitalism is more popular in Columbia. All the countries(except French Florida) are somewhat more agrarian and suburban than Europe, as is inevitable with lower population density, but Canada and Columbia industrialized more quickly, as they both had tariffs applying to their regions. In addition the most rural areas at the center of North America are not the "heartland" of their countries, instead they are the borderlands. There was a culture of abhorrence to hierarchy in America, though more reflective of European-style socialism than the OTL American variety. Hierarchy is viewed more favorably in French Florida, Columbia, and Canada, which were spared revolution of either the OTL American kind or the Soviet kind.