For those who fought at the Battle of Agincourt, the motivations would have differed depending on a number of things. For the English leadership, the motivation was to plant King Henry V on the French throne, or at least grant the English sovereignty over Aquitane and some other French lands. In 1414, Henry and his council of lords were ready to settle their dispute with the French who seemed to be prepared to make peace by granting the English Aquitane, paying them a hefty tribute, and granting him marriage to the French princess, Catherine. When negotiations came to a halt after French leadership mocked the English king, it seemed that the issue would only be resolved on the battlefield. Therefore, part of what drove the English to this fight was their motivation to defend the honor of their king and country. Of course, many also hoped to extend their own feudal holdings into new French lands. For the French, their motivations were much simpler. They were defending their own kingdom from English invaders.
Most of the rank and file of the armies, including the English archers, had no claims of nobility. Many were obliged to take up arms due to their feudal ties to their lords who called on them. However, both sides also raised their armies by paying their soldiers to fight. Therefore, the motivation was greatly monetary for the lower classes.
As autumn began, Henry decided not to take his army back to England for the winter. Instead, he chose to march it through northern France to demonstrate the power of his army's presence and maintain his claims on the French throne. It was during this campaign that the two armies met at Agincourt.