I’ve done a couple previous versions, but here’s another shot at a more “realistic” version of the second alternate world in Charles Stross’s “Merchant Princes” series.
(As always, OTL=our time line)
In this world, the French, with the aid of a more successful Jacobite uprising, succeed in doing Another Armada in conjunction with the Spanish fleet. The Hanoverian monarchy flees to America, where they are taken in by colonials quite uninterested in becoming loyal subjects of the Young Pretender, and are followed across the ocean by a number of similar-minded Brits, and, for that matter, Scots.
It would be not particularly difficult for the French, in conjunction with the Spanish and a loyal Britain, to crush Britain-in-Exile in the mid-1700s, but unfortunately, King Charles is not a well-loved monarch, and requires the frequent assistance of French bayonets to retain his throne, while the Dutch, Prussians and Austrians quickly kiss and make up so they can prevent French hegemony. All this keeps France busy enough that New Britain is not only able to survive, but even expand at the expense of French Canada.
The French manage to take down their various enemies piecemeal, and King Louis the Scholar (generally considered the first of the Scientific rather than “Enlightened” Despots) finally puts the Matter of Britain to an end by breaking up England into chunks, the Jacobian kings being foisted off with the throne of Ireland and northern (and mostly) Catholic Scotland, and occupying the SE permanently, but by then a great deal of time has passed: it was the second half of the 19th century, and New Britain had grown most formidably.
In a series of wars over the next century, New Britain, taking advantage of unrest in the Spanish colonies, succeeds in expelling the French and Spanish from North America, and with their Brazilian allies, quite a bit of south America: and with their Japanese allies (who had allied initially to avoid being swallowed by the French) made themselves masters of most of East Asia. On the other hand, the French managed to shut the New British out of Africa and India, and strengthen their European position by putting yet another branch of the Bourbon family on the Polish throne and making that flabby nation into an industrial power: and the Spanish absorbed the Brazilian homeland, and managed with French help to consolidate their position in South America.
Today, an uneasy peace has prevailed for a couple of generations. Science and technology is a bit backwards, most of it on a 1930s level, although there are some surprisingly developed mechanical calculators, and some other advances to be mentioned below…
The Empire of New Britain is probably the strongest single nation on Earth, although logistical considerations make the liberation of the Old Country still a dream. 1740s colonials were welcoming enough, but although seeing the value of a more centralized state in the face of the French enemy, weren’t interested in subjecting themselves to King Stork, and Parliamentary supremacy remains in place, although the king has some real power still. The franchise remains restricted to property-holders, although well-off women of the age over 25 were finally allowed to vote in the 1990s. Laws are harsh, the security forces are powerful, and the whole set up is a bit “Prussian.” Although there has been less immigration (Catholic immigration from Europe remains severely restricted), birth rates remained high longer than OTL, so North American populations are not much lower than OTL: given the more backwards agricultural technology, farming is more extensive and in some ways intensive than in our world, although famines are as yet not a danger (although Malthus was not born in this world, an equivalent of his theory and his gloom-and-doom successors do exist).
The Kingdom of California, remnant of a failed Franco-Spanish effort to cut off New Britain from the Pacific, was neutralized as the result of a 1903 peace treaty, and its mixed French-Spanish-British population have their own German-descended monarch and cordial relations with their giant neighbor.
The Brazilians detest Spain, but doesn’t mind the French that much, and often are annoyed by their big ally’s anti-Catholic attitudes. Japan, the more powerful of New Britain’s allies, is an aristocratic, corrupt and politically turbulent oligarchy, and the French have been for some time been trying to woo it away from New Britain with promises of total mastery of East Asia. The Japanese, who find the Koreans and the Vietnamese enough of a pain, tend to eye-roll in response. In China, the Zheng have replaced the Qin, but remain too weak to successfully repudiate their “protectors”: given that the French and the Russians are uninterested in China emerging as an independent power, the Zheng hold tight, try to build up local industry, and brutally crack down on local xenophobic and apocalyptic revolutionary movements.
The Empire of Persia, with different leaders from the late 1700s than OTL thanks to butterflies, has benefitted from French support in their “nibble away at Russia from the margins” approach, and in the last century has emerged as a major regional power, playing the French off the Russians to maintain a certain freedom of action, expanding into India and at the expense of the Ottomans during the last Hungarian-Ottoman war. As oil becomes more important in modern warfare, the relatively oil-poor French-dominated Catholic Block has been pushing hard for exclusive concessions: there is great opportunity here, but also great risk.
The Dutch Cape territory was a long time back swamped by French, Spanish, German Catholic, and etc. settlers: a small remnant survives inland in an alt-Boer state. Most of Africa is French or Spanish, although the slower pace of French colonization compared to our Scramble means that some African states have survived as puppets (or, in the case of the Islamic Federation, not worth the trouble). Napoleon never having existed to invade the Nile, Egypt is still ruled by the Mamluk slave dynasty, now getting their marching orders from Paris rather than Constantinople.
Russia, the last competitor for supremacy on the European continent, was a tough nut to crack. Polish lack of cooperation did not help (after squealing for help after Russia nabbed a third of their country when they tried to reform themselves, the Polish nobles promptly invited the Russians back in when the French prince they had put on the throne seriously tried to clean the place up), and it was a hard place to invade (Louis the Big-Headed had a really “Give me back my Legions!” moment when the French-Polish Grand Armee he had sent into Russia fared about as well as OTL Napoleon’s). And from the mid-1800s on there were serious American distractions. The general principle in dealing with Russia over the last century and a half has been containment and picking around the borders: this had some success, with a solid line of French allies containing it from India to the Baltic, but Russians have been Breeding Prodigiously since the 19th century, and even a shrunken Russia is looking increasingly dangerous: some talk of using modern arms to crush the Russians once and for all, others of kissing and making up with the Russians before the often feared Russian-New Britain alliance becomes a reality (that, however, will require selling out the Cossacks at a very minimum).
The Ottoman Empire, slower to modernize with less immediate threats in the absence of a Muhammed Ali and a Russia tied up in Europe, ended up getting rather badly kicked around in the late 19th and early 20th century, and is nowadays a French satellite. Greece, which owes its existence due to certain Philihellenist French nobles and officials, is now generally considered to have been a Bad Idea, pro-Russian, politically turbulent, and always pushing for the “liberation” of other Greek territories. Poland has industrialized energetically in the last half century and is now only second to France itself (and Russia, of course) as a manufacturing power in Europe, while Spain is currently in the midst of a bit of a cultural blooming, albeit hampered by Portuguese terrorism.
European governments are generally scientific-despotic, bureaucratic absolutisms with a technocratic slant, led by theoretically absolute monarchs whom in fact have to manage a certain balance of power with the great industrial combines, the secret police, the army, the immense bureaucracy, and the politically weak but proud and prickly scientific/technical establishment. Most of Europe is united in an economic union and military defense pact referred to by the New British as the “Catholic Block.”
European population growth has been hampered by a slower development of modern medicine, but most of Europe has only just hit demographic transition: France is more populous than OTL 2010, and is dependent on imported food. Paris is a sprawling monster larger than OTL 1930s London or New York, and all the languages on Earth are to be heard in its streets. There was no Baron Haussmann, but the Savants working for the principles of Scientific Despotism have similarly redesigned old Paris into a city of vast, straight open avenues easily accessible to artillery fire.
France is still glorious, but it is a nervous glory. It faces powerful enemies, and although Poland and the Spanish Empire have grown considerably in strength over the last century, its other allies are relatively weak reeds. Even right next to the heart of its power, the Empire must accept the autonomy of the neutral but economically powerful Protestant League, which for decades before the Great Compromise was a bleeding sore within Catholic Europe. It is perhaps no wonder that France has secretly abrogated the Pact of 2003 and begun to quietly build the Corpuscular Weapons that both France and New Britain agreed were too terrible to use. Unfortunately, New British spies found that out a while ago, and Steps Are Being Taken…
Note that this world diverges from ours before the republican revolutions of OTL: even constitutional monarchy is considered dangerously liberal by European standards, and although there are some republican movements, without a success like OTL's US to point to, they remain mostly ineffectual. There are various labor movements arising as OTL from the harshness of the industrial revolution, but only the most radical want to get rid of a monarch entirely (and only some of those are republican- the biggest revolutionary worker's movement in Russia is no-bones-about-it theocratic...)