How did the Lusignan family’s dispute with King John involve Philip II Augustus?

The dispute between the Lusignan family and King John of England arose after John married Isabella of Angoulême in 1200, despite her prior betrothal to Hugh IX de Lusignan. This action prompted the Lusignans to rebel and appeal to Philip II Augustus, the King of France, in his capacity as their overlord.12

As the French sovereign, Philip II summoned John to appear before the royal court to answer for his actions as a vassal of the French crown. When John failed to comply with this summons, Philip II pronounced John’s French fiefs forfeit in April 1202 and took military action to enforce the sentence. This conflict led to a broader war that resulted in the collapse of John's power in Normandy and the loss of his other French territories, including Anjou, Maine, and parts of Poitou, to the French crown.21