@BBadolato
Very roughly : Estates Generals weren't really considered as popular or even upper classes representations but more as lay councils divided by language until the early modern era (Oil and Oc Estates) gather by the king as sort of big extended council and echo chamber, then used by nobles to temper monarchical tendencies. It wasn't until very late that they were seen as actually representative institution.
Provincial Estates (formally, Estates Generals of [X] province) were more regular and common, had a more important fiscal relative autonomy but limited to
Pays d'état and shouldn't be confused with
Parlements that weren't considered as representative at all, but part of the royal administration having essentially a judicial role dominated by Paris.
French and English were, obviously, very different institutional kingships even by the Late Middle-Ages (and before, would it be only because the French king was sacred, and not just crowned) and many of their institutional features illustrate nevertheless f the fact medieval royal hegemonic (monarchical power is really, as itself, appearing in the modern era) were as much fought against than trying to institutionalize themselves outside kingship proper.
Basically, you have as much an history (rather than tradition) of strong royal power emerging in both England and France (
as well in Germany but it was knowing a lot of drawbacks until 1648) but as well an history of struggles against this emergence (would if be feudal, aristocratic, bureaucratic, intellectual, clerical, etc.).
I said "rather than tradition" because it wasn't part of medieval socio-cultural cores : the yerosolemite kingship was considered as "idealized" feudality from the beginning and while being largely French, never really went trough the same solidification and hegemony of power benefiting to the king. Even in a later stage, I doubt institutions would be seen as an exportation (after all the Kongo Empire didn't pulled an institutional Mejii even after being vassalized by Portugal)