You know what? I love the idea of them finding out about the Directory's plans and then uprising on the 9th, just to reverse the trick.
Socialist Republic of France? It'd be an interesting idea, especially if it survived. The question is how does it evolve. I mean, Babeuf was explicitly a fan of equality of outcome, which would cause some issues if people decide to not work (and that number became statistically significant). I suppose it would depend on how they'd approach a solution - a concept of national service? Working Unions?
I'd be curious to see how it is resolved, because if you insist on national service, you could very well have them have a process of "Validation", where a clerk is set up to basically say "Yeah, nah, they've done their job", which qualifies them to continue to get their accommodation, rations, etc.
Another concern is with trading with the outside world. I don't know who France owed money to, but a good way to get others on your side (and undermine the French Monarchy), would be an agreement to renegotiate the crowns debts with important external debtors (i.e. The British). Socialist Pro-British France that agrees to take ownership of the French Crowns debts? If it can service the debts it chooses to honour to external parties, then it could avoid the Napoleonic Wars.
The final of the trifecta of "God make those work" is whether those parties that Babeufist France agrees to trade with can stomach a level of reform to prevent revolution. The concept of "National Service" isn't hard to fulfil - you join the army, or pay your taxes. But you do that at the expense of the crowns opponents, and you could feasibly maintain most of the British System (and get a potentially massive army at the same time). It could be a way to increase the power the crown to a scary degree - essentially re-enclosure, and whilst on the cusp of the Industrial Revolution - meaning that the Crown could essentially make bank itself.
It'd be a VERY different TL - especially if it was only "France", and "Britain" that had these policies applied, but not the colonies, where being deployed could count as a way to be "Validated".
Huh. Complete Brain-Dump but there you go.