I`m sorry to keep contradicting you, but Thomas du Perche and the Anjevins were both descendents of the House of Chateaudun, there was a third line that of the Vicounts of Chateaudun which survived until 1249. King John of course died in 1216.
There was also the Angevin Line of the Kings of Jerusalem, descended from Falk.
They did go extinct in the male line in 1186, but I don't think King John was at fault.
In the female side of the line we get Isabella, Maria, Isabella II then Conrad IV and Conradin. While it is questionable that they counted as Plantagenets, They were closer relations to the Plantagenets than was Thomad du Perche. Fulk being the father of the first Plantagenet.
edit the Angevins went extinct in the male line in 1185.
https://en.wikipedia.org/wiki/House_of_Châteaudun
https://en.wikipedia.org/wiki/Kings_of_Jerusalem_family_tree