Philip Augustus and Arthur of Brittany seal their alliance by marrying the Dauphin Louis to the princess Eleanor, Arthur's sister. When the time came to challenge John for the English throne, he'd have a far more legitimate claim to do so.
How to get a Plantagenet on the throne is the harder challenge. Perhaps Louis after his conquest allows the young prince Henry (OTL Henry III) to retain some fiefs of his own: maybe Tourraine and Maine to provide a buffer between the expanded royal demesne (now including Brittany, Anjou and Normandy) and the troublesome lords of the south, and most likely the succession to his grandfather's county of Angoulême. A generation or two later and the French-born Plantagenet is "elected" King and pushes out the tiresome Capetians who keep draining the land for their wars in Wales and Scotland. Transition could be made easier if OTL Henry III marries into the Capetian house.