There are quite PODs to reach this goal (victory in the battle of Lincoln, no Henry III, John doesn't die this quickly...) , but let's say that by 1218, Louis, the elder son of Philippe II Auguste (OTL Louis VIII), is King of England, and firmly in control of his kingdom.
On the short term, we can assume Philippe II still dies in 1223, and Louis in 1226.
What can be expected of this situation?