As it says on the tin.
The First Baron's War was an uprising in England that resulted in the invasion of England by Louis VIII of France and Alexander II of Scotland from 1215-17.
http://en.wikipedia.org/wiki/First_Barons%27_War
Louis VIII (then a prince) occupied London, and was proclaimed king by the English barons. He also received support from the King of Scotland in return for possession of his claims in the North (Northumbria, Cumbria).
So, what does it take for the French prince and soon to be king of France to win? A successful siege of Dover? John simply to live longer, thus those who hated him to not shift their allegiance to his son?
If Louis won, and became the King of France and England, this would undoubtedly rock western history! Scotland would dominate the north of the island as a French ally, and France would rule the rest of the island from Paris. More French would come to influence England and its language, similarly as to what happened 150 years earlier in the Norman invasion. Could the French hold England? If they do, how does this affect the balance of power in Europe?
It's a very juicy piece of AH that I think has largely been ignored, and is certainly worth discussion.