The Norman conquerors of England gradually became Anglicised and developed an identity seperate from their French roots. They never set out to make England subject to France,
…but to rule it for themselves as oppose to the Saxon peoples. The Norman kings founded the Plantagenet Dynasty, Norman nobles intermarried with members of ruling Saxon houses, and in time they came to regard themselves as English. So they never came to an abrupt end, the Norman identity just gradually faded into being Plantagenet English. The Plantagenet Dynasty ended in 1485 at the Battle of Bosworth, when King Richard III was defeated by the combined armies of Henry Tudor and Rhys ap Thomas, both Welshmen who were cousins. This ushered in the Tudor era, with Henry taking the English throne and incorporating the Welsh Dragon into the British coat of arms. (MORE) 
