The Kingdom was a rather unstable entity, being a collection of territories with various cultures and levels of autonomy, their only link being an Oath of Fealty pledged to the French king whose only true authority only extended over a small parcel of land known as the Royal Domain.
The king lost much of his northern vassals during the War of French Succession and his southern ones following the failed Albigensian Crusade. Fromt then on, the kingdom's territory was slowly eroded by its neighbours until all that was left was the royal domain which was simply absorbed by another kingdom when the last king died without a male heir.
Ther term "Demesne" (old French for domain) has been revived in recent years by touristic organisations who trade in the region in and around Paris. It is however a strictly folkloric designation as the national government never gave it any form of official recognition. Also note that the term is rather loosely applied with some towns outside the historical Royal Domain being included due to the presence of peoples who self-identify as "Demesnians" while other which were within are excluded due to a majority within of "foreigners".