AHC/WI: Parliamentary Ancien Regime that survives until the present

How could the Estates-General evolve to take on the same role as the Parliament of the UK, so that Kingdom of France becomes a constitutional monarchy with parliamentary supremacy, and how could such a system last until the present day? What might a modern Estates-General in a parliamentary French monarchy look like?
 
It would take Henri III or IV turning their calling into a regular practice instead of something exceptionnal it was in OTL. (There's a bit the part that after the Religion wars, there are a lot of untolerant ultracatholics). Have someway the États Généraux endorse fully the Édit d'Amboise (which was identical to the Édit de Nantes, but was started by Henri III, which never had the power to make it real) would increase their prestige, and could help long-term.
 
Estates Generals becoming a regular institution was discussed by french elites in 1789, but couldn't be really realistic, because of the rivality with other traditional overlapping bodies and jurisdictions juridictions (and that's a simplified map)

French Parliments were judicial institutions, with limited autonomy (both because of the parallel power of provinces and généralités, and because of the technicall supremacy of Paris Parliament)

Eventually, it was way easier, in order to reform French institutions in the XVIIIth, to simply get rid of everything and begin from scratch (well, relativly speaking).

Now, if you're discussing of an earlier PoD, it could be possible during and/or directly after the Wars of Religion with a weakened Valois dynasty.

More factionalism amongst nobility would probably see an uneasy alliance akin to the IOTL Fronde, but with more chances of success in this context.
Basically nobility and parlementarian elite calling for regular EG (but not permanent at first) as the rule and no longer the exception.
The diversity of Parlements could be as much as an obstacle than a motivation to this evolution, especially with the idea of a common body for all the kingdom, but eventually your goal is to keep them as much as possible while having one permanent EG issued from them.

It wouldn't be a constitutional monarchy, more obviously a parlementarian monarchy while itself far from being akin to IOTL British parlementarian monarchy but as the latter, it could provide the structures to evolve more liberaly.

DracoLazarus : Don't forget that EG were essentially the body of nobility and elites, more or less opposed to a more important royal authority (there's a reason why Bourbons carefully avoided to gather them). It asked for strong kings and favourable situations to ride them where the king wanted to see them (and that's as less parlementarian it could realistically be). In other contexts, critically with more troubled times it could easily backfire (and God, it often did).
 
How could the Estates-General evolve to take on the same role as the Parliament of the UK, so that Kingdom of France becomes a constitutional monarchy with parliamentary supremacy, and how could such a system last until the present day? What might a modern Estates-General in a parliamentary French monarchy look like?

Highly unlikely. Unlike England, France's Estates-General never really had an opportunity to come to power. France's Kings already had the ability to raise taxes on their own and without a civil war constantly draining resources (the religious wars of the 16th century) then there would be no need to call the Estates. According to Wikipedia " had no true power in its own right—unlike the English parliament it was not required to approve royal taxation or legislation—instead it functioned as an advisory body to the king, primarily by presenting petitions from the various estates and consulting on fiscal policy". So clearly the Estates-General never had the power or opportunity to develop into something similar to England's Parliament.
 
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