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).