The French are their western patron. France has little direct interest in the pacific as Europe is basically their colony, but they want to block British and Russian expansion in the region.
Napoleon III still gets the throne and he's still the wiley bastard as IRL but with a significantly larger army and treasury to throw around.
As for China, I could easily see them trying to defend Korea despite falling apart in the 1860s (like Second Opium War irl) and losing so badly they are forced to cede half of all manchuria to Japan as they did Russia IRL.
Why would Napoleon III still get the throne if Napoleon I succeeds? Napoleon II doesn't get sent to Austria, which might butterfly away the tuberculosis that killed him OTL, and Napoleon stays married and in proximity of his wife, meaning he could easily have more children. And those children wouldn't have to try to rebuild France's prestige (heavily degraded by the collapse of its continental empire and Britain eclipsing France) via harebrained foreign expeditions.
I'd argue the pressure is still there. They still witness the first opium war and see how a tiny island on the other side of the planet utterly stomped the Chinese.
In fact the opium war can be even more humiliating for china than IRL as Britain forces them to be their preferred trade partner to make up for loss of market influence in Europe.
China getting stomped in the First Opium War didn't elicit much of a response from either Japan or China though. For Japan, they saw it happen, had the Dutch warn them to open up willingly or risk getting open up by force as well, and still didn't open up for another decade until the US came with the Black Ships. For China, they didn't start their Self-Strengthening Movement to reduce the gap between Europe and China until the 1860s, after another Opium War and a series of major rebellions like the Taiping and Nian Rebellions. China being defeated militarily by much smaller nations is nothing new (all the northern nomads, including the Jurchen and Manchu ancestors of the Qing) and they also haven't had the best naval track record either. They just usually dealt with it by paying the invaders off with tribute or some other concessions. The extent of the problem only became apparent after decades of increased incursions forcing changes to China's internal laws and social norms and the central government's inability to prevent those changes from being forced upon the empire.
Plus, there's no guarantee that the Opium War would even unfold in this TL. The OTL First Opium War was hugely controversial (the antiwar faction's motion failed by 9 votes, 262 votes for vs 271 votes against) and diverting more of Britain's fleet away from its already established interests in India while the French have previously threatened said interests via proxy wars in India and the invasion of Egypt would make it even less prudent to go to war with yet another major power (the British didn't have a clear picture of Qing weakness before the Opium Wars, IIRC).
Korea is a must, it's seen as a dagger pointed at Japan and is needed for security.
Otherwise I don't know how much they wanted versus how much they thought they needed to get respect as an equal to European colonial powers.
According to Duus, "dagger pointed at the heart of Japan" was due not only to Korea's proximity to Japan, but also its weakness on the world stage. Meiji leaders were interested in "the maintenance of Korean independence," which required self-strengthening and reforms that the Japanese had implemented and would attempt to influence/force Korea to adopt in turn, rather than simply economically and militarily dominating the peninsula.
OTL Japan's initial motivation for taking Korea was because of the threat of Europeans (specifically Russia) using Korea as a staging point to threat Japanese interests, not because Korea itself was inherently a threat. The debate on whether to invade Korea in the 1870s was not one of conquest, but rather concerned a potential punitive expedition to force Korea to recognize the Japanese emperor instead of only the Chinese emperor, plus trade relations and such. A reordering of the old order, not a redrawing of the map, as it were. It was a minority opinion, regardless, and one without set plans or a unified goal. And when they did dominate Korea fully, they were satisfied with leaving it as a protectorate for a fair bit, rather than impose direct annexation.
The main issue was that Korea was seen as too weak to protect itself (not least due to the reactionary tendencies of the Daewongun, who dominated Joseon politics for a good part of the 1800s, and the factional conflict within the Joseon court itself) and their attempts to balance the Chinese, Russians, and Japanese off each other was seen as threatening to Japanese interests since it could've seen the peninsula fall under Russian domination (after the assassination of Queen Min, King Gojong took refuge in the Russian legation, for example). Plus, Korea had already been subject to punitive expeditions by the French, Americans, and Russians previously, so they saw it as a threat that only increased in magnitude over time.
Even in the 1880s, Japanese leadership hadn't decided whether to commit to a passive, nurturing role to encourage Korean reforms or to be aggressive and interventionist to force reforms. Actually dominating the peninsula was not one of the options at that point.
Japan started the Meiji Restoration in 1868 and annexed Korea in 1910, so it took 42 years to build up enough strength to impose itself on Korea while Korea largely stagnated. If Japan modernizes faster and tries to force Korea open before the Daewongun takes power in the 1860s, that sets the stage for Korea to not be as weak as it was OTL before Japan starts seeing Western imperialism as the only practical world order and one that they had to partake in.
As I said, that they can take. They won't be able to swallow all of China, but whatever they can take, they will take. The markets of China are too important for Japanese economic growth to leave to anyone else.
According to Duus in
The Abacus and the Sword: The Japanese Penetration of Korea, 1895-1910, the initial response in Japan to China's defeats at the hands of the British in the 1860s was that "the revelation of Chinese weakness promoted the idea that Japan and China, which were as 'close as lips and teeth,' should stand together to defend East Asia against the intrusions of the predatory Western nations. But gradually, since China remained unable to prevent the Western nations from nibbling away at its borders, the Meiji leaders grew more ambivalent toward their largest neighbor. From the late 1870s, they began to regard the Ch'ing empire as their principal hypothetical enemy" [21, 22].
Basically, it's only because the Qing kept losing over the course of several decades and could not be regarded as a great power ally that the Japanese reevaluated their stance towards China. If the timetable gets pushed forward for Japanese modernization, then there's nothing really pointing to Japan not allying or supporting China and Chinese modernization to try and resist Western imperialism in the manner they tried to impose on Korea during the late 1800s before they lose all hope in China actually being a viable ally. It's far less costly to Japan to gain concessions that way than to force China at gunpoint and garrison their new holdings for fear of a reversal later, after all. That was the Japanese approach to Korea until Japan managed to force the Chinese and Russians out and had already gained so many concessions and business interests over the preceding decades (plus the relative stagnation of the native Korean economy) that direct annexation was economical.
All this to say, expansionistic Imperial Japan, at least the way Peter Duus put it, wasn't inevitable and was informed by the behavior and conditions of neighboring nations and Western expansionism. Curb the latter and see the former reform faster (potentially with Japanese assistance) without Western pressure bearing down quite as fast and East Asia might've avoided the worst of the atrocities of the 20th century.
