There is no reason to think the Plantagenet yDNA changed after Edward III. Edward III was a maternal grandson of Philippe IV. Their yDNA would not be the same, except by coincidence.
The Plantagenet yDNA is unknown. Some people think it might be R1b-U106 based on triangulation. Some descendants have been tested, but the results are being withheld pending test results on Richard III. William the Conqueror is also speculated as R1b-U106.
The Tudor yDNA is speculated as R1b-L21.
You can read about the yDNA of British kings here:
http://www.surnamedna.com/?articles=y-dna-of-the-british-monarchy
There is some doubt about the yDNA of French kings. A test on a handkerchief dipped in the blood of Louis XVI showed G2a, but tests on modern descendants showed R1b-Z381. Some people think the handkerchief was contaminated. Others think that Philippe I of Orleans might not have been the biological father of his children.
You can read about the DNA of European kings here:
http://www.eupedia.com/forum/threads/25236-Haplogroups-of-European-...