At which battle was the Black Prince's army crucial in capturing Jean II of France?

The correct answer is indeed the Battle of Poitiers, which took place in 1356 during the Hundred Years' War. This battle is significant not only for its military outcomes but also for its political ramifications. The Black Prince, Edward of Woodstock, played a pivotal role in leading the English forces to victory against the French army. His tactics, including the effective use of longbowmen, contributed greatly to the English success.

The capture of Jean II of France was a major blow to the French due to his status as king and the strategic disadvantage it imposed on France. This event had lasting implications for the conflict as it galvanized English claims to the French throne.

In stark contrast, the other battles listed—Agincourt, Crécy, and Waterloo—occurred in different contexts and periods. The Battle of Agincourt, for example, took place in 1415 and is celebrated for its own significant English victory, while the Battle of Crécy, occurring in 1346, was one of the earlier conflicts of the war but did not involve the capture of King Jean II. The Battle of Waterloo, fought in 1815, was unrelated to the Hundred Years' War and involved different nations and military strategies altogether.