Trimerica
In this world, Napoleon chose not to re-establish slavery, mollifying the plantation owners with massive land grants in the Louisiana Territory. Resources were poured into exploration, colonization, and development. This effectively split the United States off from the rest of the continent. The western territories remained in Spanish hands, until various revolutions and wars of independence created multiple nations from the Rio Grande to the Yukon.
The nation of Napoleonica seceded from France in 1871, with relatively little fuss, and includes much of the original Louisiana Territory, plus most of what would become Texas and New Mexico. It is of course closely allied with Quebec, which is an independent nation. The eastern portions of Canada were absorbed into the US following a series of wars and reprisals in the 1840s.
With abolitionism in both the west and north, the southern United States saw the impossibility of their situation and slavery in the US was outlawed in the 13th Amendment, which in this case was passed in 1834 and somewhat differently worded. Full racial equality did not immediately follow, of course; voting rights were granted on a state-by-state basis, much as they were for women. The 17th Amendment, passed in 1891, made suffrage universal for all adult citizens 21 and over, but again, the de facto and the de jure took quite a while to sync up.
Napoleonica
With some of the most fertile land on the planet, and the mineral resources of the Rockies, Napoleonica was set to become an economic powerhouse, except for the limited port access in New Orleans. One port, easily blocaded, worried France. From 1820 to 1830, a series of wars were fought over the western half of the Gulf of Mexico, until most of what would become the Texas coast, and then inland regions, were seized, becoming the Province of Josephine.
Europe
The shuffling of noble bloodlines and alliances over time has created a very different Europe. A Communist revolution in Germany in the 1840s drew England into a bloody and ultimately futile war, leading to widespread anger over the perception the Queen was influenced by her husband to send British troops to reclaim his homeland. The monarchy was dissolved and, in an effort to forestall a similar revolution in England, more rights were granted to commoners, along Chartist lines. Russia managed a similar defusing of populist sentiment without giving up its nobility, ending up with a more constitutional monarchy. (The lack of Victoria's offspring interbreeding with the many noble houses of Europe also produced physically healthier royals.)
Asia
It was Alta California which opened trade with Japan in the 1860s, leading to similar consequences and the Meiji Restoration. By this time, India was seeing it was better to colonize than to be colonized, and with the British Empire effectively gone, had begun seeking control of Chinese trade. The Sino-Indian wars for control of China went on for several decades, with China finally driving out foreign occupiers in the 1930s and establishing a strongly nationalistic government with a powerful navy.
Present
The current year is 1980, and perhaps the most glaring difference is that there is no development of atomic power or weapons. Physics, in general, is a TL behind, and while there are many practical inventions from radios to x-ray machines, there's a lack of an overall unifying theory or understanding of many phenomenon. Engineering and "practical" science take precedence over theory in most nations, and "if it works, who cares how?" is a common refrain.
Overall, the world is TL 6, but it's a rugged, heavy, TL 6. On the plus side, there were never any wars on the scale of World Wars One and Two, and much of the technology discovered to fight them was developed later or more slowly. On the minus side, the world is, on the whole, more isolationist and protectionist; less trade means less competition, which means, fewer incentives for industries to seek to improve.
Comments
Author's Notes
This is a background world and, as such, represents zero effort on my part to craft a fully worked-out and compelling AH. Skim a little wikipedia, make up a few things, boom, done. Rest assured, all effort was spared in terms of accuracy and plausibility.