[sidibe]

Killing Louis didn't lead to less authoritarianism it led to Robespierre and eventually Napoleon. Most of today's liberal democracies didn't come from revolution or civil war but from foreign forces deposing tyrant or peaceful transition. This includes France which only became democratic after Prussia ended Napoleon III

[yywwbbn]

Yes, the transition wasn’t very smooth though. In cases with little foreign interference, it was more like:

Absolutist monarchy -> violent jacobin style revolution -> ??? (a lot of war and dead people)-> reactionaries come back to power -> a more moderate revolution/coup which brings a more balanced regime which establishes some kind of a rule of law based constitutional order.

Britain only had a single cycle of this, while France needed 2/3.

It not like the goal of Prussia was to establish a democratic regime in France, that was just side effect and arguably Napolean brought that war on himself (just like his uncle did with Russia)