I have read some of Robeson's "Celstial Empire" ( [link]
) short stories with enjoyment - it's a series set in a world where the Ming kept sailing and ended up dominating the world - but I couldn't buy the Aztecs as the main opponents (the Aztecs apparently manage to develop steam powered tech by the 19th century on their own...serious, serious levels of wankery involved). So, evil Frenchmen instead (which people of certain political inclinations will also find unbelievable.
I took some elements from Nugax's (soc.history.what-if map beast) excellent Song Industrialize map and from the GURPS Ming-3 scenario. The Chinese aren't quite as territorial grabby as in GURPS, and anway don't seem to be so in Chris Roberson's novel, either: they tend to rule through vassals rather than large-scale territorial conquest, as far as I could tell.
The Spanish and Portuguese got kicked out of Asia and the Americas for misbehavin', and the rise of the Netherlands got butterflied away: by kissing ass the British managed to avoid getting wacked by China, and eventually built up an empire in Eastern (non-Chinese North America) and Africa, while the French concentrated on building their dominance in Europe. (With, alas, the Chinese frequently meddling once non-French nations discovered that petitioning Beijing could bring results). A richer and (thanks to frequent practice fighting Europeans) rather more gunpowder-weapons-savvy Ming China managed to hold off the Manchu, and eventually (rather later) conquer them outright.
Social and economic changes and a long line of do-nothing emperors eventually led to a change in dynasty, but the throne remained in ethnic Han hands, and breakaway vassals and territories were soon brought to heel. A slow-takeoff industrial revolution got underway, cross-fertilized by European ideas and developments (Europe in turn was somewhat slowed in its scientific revolution, oddball Chinese ideas having led thinkers off on several tangents).
The most troublesome of the Vassals required a major war to defeat, but in the late 1800s the British were brought to heel, their empire broken up, and their American territories split off as a seperate vassal. The French were a tougher nut, but the French Empire's efforts to unify Europe were ultimately stymied.
As a result of the "era of European humiliation", rising anti-Chinese, anti-monarchy, racist-scientific movements came to the fore in Europe over the next decades. In the 1960s the Pan-Europeanist Revolution overran France and its German and Italian territories, and similar movements came to power in Iberia and Scandinavia: in the subsequent First European War, the Chinese Empire and its still-loyal vassals, facing mass-conscription armies equipped with such innovations as barbed wire and "mobile fortresses", were driven to the fringes of the continent. A generation later, the Northern Fusang European colonies rose in revolt against the Empire, and the second European War broke out. Project Loutre-de-Mer ultimately failed to conquer (or "liberate") Britain, but European forces successfully crossed the Med and took NW Africa, although their advance ultimately stalled out in desert battles. And the NE of America fell into the hands of pro-Europeanist forces.
The line have been drawn, and the Chinese have been forced to commit more of their resources to a "cold war" in which they must constantly struggle to surpress European subversion among their vassals.
The Islamic world is generally fairly loyal: from the days of the first great treasure fleets, Muslims have often played an important role in Chinese military forces, and their influence at court has helped keep the relatioship between the Empire and its many Muslim vassals and subjects a cordial one. The Middle East has done better than in our world, and the universities of Cairo are one of the world's leading centers of science. Many Muslims hope to one day convert the Emperor himself, and with him the Empire: however, few upper-crust Han are really interested in following the commands of an Arabian camel-merchant, and some emperors have sponsored a Buddhist revival which competes with Islam for hearts and minds on the outskirts of the Empire.
Africa remains a bit chaotic.
The Han Empire is despotic and tradition-bound, but on the other hand is also meritocratic and non-racist and in its own way rational, and the Imperial hand is quite light in much of the world. The "Union of Western Nations", on the other hand, is a *Fascist regime, "scientifically racist", and organized with Prussian ruthlessness wherever it rules. The Iberian and Scandinavian states are almost as unpleasant, while OTOH the North American Federation of Vinland, if highly Asian-xenophobic and dominated by the Liberty Party, has rather more of a civil society and laws which aren't so easily tossed aside in the name of State Security. Engineering a split between Vinland and the UNO is one of the major aims of Chinese security and diplomatic forces, but is complicated by the fact that the Vinlanders would probably require all of New Albion as a quid pro quo...
Technology is generally behind OTL, with engineering generally around a 1950s level in the 2020s and abstract science a bit further back, with agricultural science a bit ahead. Han architecture and engineering tend towards the baroque, while western Europe tends towards the grimly utilitarian and "scientific-rational" (for all their superstitions on Racial Destiny, it is an article of faith in the UNO that they are scientific and rational while the Chinese are superstitious and old-fashioned).
Currently a contest is ongoing between China and the UNO and allies to be the first to put a man into space: the Chinese have rather more resources, but are being hampered by the crudeness of their calculating technology (Chinese statisticians and scientists remained dependent on large numbers of men and women with abacuses long after mechanical calculators came into general use in France). In the meantime, Chinese spies (drawn from their roundeye vassals) are busy following up odd rumors about new discoveries in physics in Vinlander laboratories...