I'd say the most likely difference between Lutetia and Paris would be that Lutetia never really got demolished and rebuilt like Paris did. So it lacks the boulevards that make it so difficult to hold in a revolution.
At least, that would be my explanation for the Lutetia Commune not getting killed, and it would make sense; the monarchy never returned, so never tried to prevent another revolution.
Notably, making it easier to kill rioters wasn't the only, or necessarily even the primary, reason for tearing down medieval neighborhoods and reconstructing large chunks of a major European capital in those days.
When people say those neighborhoods were unsanitary, they don't just mean "poor people are stereotypically dirty." They can very well mean "there were literal rivers of raw sewage" and "gee it turns out that epidemics spread really fast when you have like one person living in every three square meters of floor space, who knew?"
Plus, y'know, all those winding alleyways often meant things like "no way for two carts to pass each other." Not good on that front either. A lot of Parisians
approved of the major reconstructions of the mid-century, because it meant less disease, more fresh air, and less living in the Victorian version of a favela.
...
Now, in the Gayaverse, Europa had the germ theory of disease much earlier, and that might well trigger an earlier push for public sanitation and public health efforts. But by that same token, that means you'd see a gradual process of urban reconstruction and attempts by
both monarchs
and republics to build cities that were less overcrowded, more liberally supplied with clean water and ways to get the sewage out of the way, and (ideally) more aesthetically appealing.
Paris in particular had considerable prior history of people calling for reconstruction, including during the pre-Napoleonic days of the First Republic, too. This really
wasn't just about "the Man wants to be able to fire grapeshot down long boulevards to stop rioting mobs from overthrowing him," even if that was in some cases a factor being considered.
...
Now, I actually didn't know at the time that I had "the Commune didn't get drowned in blood" as an outcome that Gallia had been one permanent First Republic throughout the past 125 or so years of its history, but in my opinion that honestly makes it
easier to explain a negotiated cease-fire, because there's a relatively secure national government
to negotiate with the Commune.
Like, historically as I remember, Napoleon III surrendered, the government that later evolved into the Third Republic formed to fill the power vacuum, but with Paris besieged in short order a
different and more socialist-leaning government emerged to fill
that power vacuum.
If the central government had been, instead,
the Republic, an institution that had existed since 1789, and which relocated the capital to a provincial city after the terrifying success of Dyskelandisch arms on the frontiers, it is still credible that working-class radicals and socialist agitators would have overwhelmed the
local government of Lutetia and mobilized the populace to repel a siege. But the idea of a cease-fire being negotiated between the Republic and the Commune seems a bit less impossible to me under those circumstances, especially if we slightly butterfly the exact political balances of power that prevailed within the Commune and the Republic.
And I don't know, I like to add happy-ish-ish endings to things sometimes?