Hi. Still catching on, getting to 1895.
So, on French politics under Napoléon IV in the 1880s and 1890s, a few more remarks.
I read that you had Freycinet as Foreign Minister during the Sino French war ITTL, being a moderate republican that eventually switched. While that's not impossible, I don't think it natural.
I don't know much on Freycinet, except that he was an engineer by trade, and his political carreer had basically begun as a helping hand to Gambetta in his efforts organizing French resistance and efforts after Sedan. Without Gambetta and without the war happening as badly as it did IOTL, I surmise Freycinet would not have had the occasion to rise above the fray and he have probably stayed in either an administrative office or landed at some private job.
The thing, given the repressive turn of 1867 ITTL and then the corporatist, proto integralist constitution of Napoléon IV, there is no much room left for the republican or liberal opposition to be coopted. Basically anyone who was a republican before 1848, who remembered the days of the Second Republic or was born early enough to be a student and radicalize with republican ideas under Napoléon III (so any republican, moderate or republican born before 1850), would not have gone along with either "Les Trois" or Napoléon IV TTL project. They would have gone with the OTL parliamentarian system set up by the constitution of 1870 under Ollivier (when Ollivier negotiated the formation of his government, Gambetta was sounded out and rather than rejecting it, was "open" to it, though that meant he demanded the powerful Interior Ministry ) if it had survived the 1870 war, but the authoritarian system under Les Trois, and the powerless parliament under Napoléon IV, would have been anathema to republicans, even those decried as "opportunistic" (coined by the radical republicans I believe, but that should be understood as "pragmatic"). Their participation would have required some political concessions, not empty ones, I think. You might have looked to the OTL program of Belleville for instance, Gambetta's plank for 1869 elections.
Instead, for Napoléon IV, I would have looked more towards conservative-liberal monarchists, especially Orléanists. Broglie, which you briefly mention as having occupied several positions, Decazes, or even Gramont if still alive (a carreer diplomat, and not utterly discredited by the war of 1870 ITTL), each of them serving at the Quai d'Orsay at some point IOTL, either under Napoléon III or MacMahon, and also all dukes. Otherwise, on more domestic matters, after Rouher, I would like into figures among the OTL monarchists and bonapartists that eventually rallied the republic in the late 1880s or 1890s, like Mackau or Bardi de Fourtou, or among those who supported the wannabe Boulanger putsch.
Unless Napoléon IV reinstated them, France did not have any property requirements since the overthrow of the July Monarchy in 1848. The Order Party under Thiers had though replaced it with a more permicious requirement on residency that eliminated a third of the electoral corps in 1850 (you needed to reside in the same place for three years to be able to vote, so if were an itinerant worker looking for job from a city to another...); that law had been a pretext used by Napoléon III to launch his coup the next year, reinstating universal male suffrage. Universal male suffrage subsisted under the Second Empire, though it was "guided" with the "Official candidacy" system. There was even secret ballot, from what I could gather, enshrined in the 1848 constitution, and though Napoléon III considered removing it, he ultimately kept it, though in its application, I read it was anything but thorough.
On the Panama scandal also, Eiffel's scapegoating seems logical. I'd say it would be even more logical, considering that Lesseps was a relative, albeit distant, of Dowager Empress Eugénie, and putting too much blame on his shoulders could have tainted Eugénie and through her, Napoléon IV. I don't recollect reading much on Lesseps' connection with Eugénie, and I guess harsh press censorship could have avoided it, but did you use that plotline in any way? I just think the connection is too tempting to make for the regime opponents to use it against Napoléon IV and the imperial regime.
That's sad for Eiffel in this TL though, since the whole scandal stemmed from Lesseps' stubborn refusal to budge from a sea level canal and the technical issues with it that were near impossible to overcome, leading to financing issues and schemes that brought about the OTL scandal, while Eiffel, an engineer by trade, advocated for locks, like would be done by the Americans not long after, but arrived in the project far too late to save it. In a thread of mine, I even discussed the possibility of removing Lesseps from the picture (getting conveniently dead), giving the reins of the project to Eiffel from the beginning, giving a working canal in the 1890s, and no scandal.