This is a very beautiful map and a pretty interesting scenario, but just one thing, which is that OTL, one of the main reasons that the Fashoda incident didn't devolve into a war, alongside the Dreyfus Affair oc, was that France did not want Britain as an enemy in the slightest. The Captain who caused the incident kind of acted on his own will, or according to some theories, on the will of some isolated general or governor. In 1894, France and Britain had started secret meetings to lay the bases of a military alliance against Germany, as their growing power scared them both.
Now, I'm not saying the Fashoda incident wasn't a big thing, or minor or anything, but people tend to make it out as that huge thing that could've caused WW1, and like, there is a reason it didn't, which is that then, no one among the parties involved wanted a war. In 1914, everyone wanted a war, Germany and A-H may have offered Europe the War, but France, Britain and Russia were more than happy to accept it with open arms.
All of that to say that, you should, imo, possibly need to have either Germany not growing as fast as a main power as it did OTL in the 1890's (which would require to not have Wilhelm on the throne so that'll be hard to do), or to get in a way things to sour as soon as the early to mid 1890's between France and Britain, as to make those meetings which lasted from 1894 to 1903, when the plans for the final Entente Cordiale including Britain were drafted, sterile. A good way of doing this could be by making Russia a bigger threat, real or in the British mind, as to, once that the alliance between France and Russia is signed in 1895, render the possibility of a Franco-British alliance lapsed, with a Fashoda incident only burying further any ideas of friendship that the two governments might still be considering.
However, I don't believe that the Fashoda Incident, even with the 1894 Franco-British rapprochement yeeted away, could lead Britain to side closer to Germany. At best, they'll see France as too arrogant, stubborn and demanding to deal with, while they'd see Germany as too powerful, too dangerous and threatening to even consider letting it continue its progress.
Because a thing people (Mind, not you in particular, just a very common trope in Alternate History), tend to forget is that not only Germany by the early 1890's is representing the biggest threat to British hegemony and the second greatest threat to Britain in the British mind (the first place going to Russia), but France has been trying to get closer to Britain as early as 1830 (granted, there were interruptions, such as from 1871 to 1887, because Thiers, MacMahon and Grévy didn't see the interest in allying Britain, were distrustful of them or just didn't gave a fuck, but with Sadi Carnot and the short lived mandate of Jean-Casimir Perrier, the interest in having Britain as a partner, at first for colonial purposes, the idea that Britain and France can help each other grab as much of Asia, Oceania and Africa as they may, and then from 1895 to 1913, when the mentality is that Britain is the only way for France to beat Germany. All the while, Prussia didn't try that much to get closer to Britain in the first half of the century, in fact the Schleswig Wars, and to an extent the Austro-Prussian and Franco-Prussian wars in 1866 and 1870 only drew Britain further from Prussia, as no one likes a rising power (I know Prussia is already a power then, read it as no one like someone important gaining more power). Granted, by 1871, a British-German alliance is still well alive on the table, and seems much more appetising than a Franco-British one, since the Empire was overthrown and Napoleon IV won't reign, but there is still the fact lying around that, well, the centuries old Franco-British enmity had its grave dug by Louis-Philippe, and then Napoleon III gladly shoved it down there. For most of the 19th century, it's not the Franco-British enmity talking, it's simply the game of Great Powers, as France and Britain did found themselves more times on the same side, may it be at war, in diplomacy or in simple ideas, than in nearly a millennia of co-existence.
End rant.