Another thing is that the Battle of Agincourt is extremely important in terms of history, considering that it brought out teh power of the Welsh Longbow. There should be considerably more that should be more important, though, and I would like to know what else was so important to the world about the Battle of Agincourt.
Actually this is something of a misconception. Crecy and Poitiers were the battles that established the power of the Longbow. Specifically Crecy. The bodkin arrows cut clean through rather poor plate armour and completely massacred the unarmoured horses. This was at a stage where plater armour had not even begun to consider the strength of a longbow. The French army may as well have been naked.
The same thing happened again at Poitiers a decade later. This time the French King was captured for ransom. However in just ten years plate armour had advanced to such a point that killing shots were hardly a given. Curved surfaces and ingenious design meant arrows often skidded off and wasted their force in the mud. Unfortunately, the horses remained manifestly vulnerable.
By Agincourt plate armour had had over six decades to react to the threat of the longbow. It had evolved in such a way as to make killing it's occupant all but impossible. Contrary to popular perception the French did not die under a storm of arrows, they died in a good 'ole melee . It was the mud, not the archers, that destroyed the French army. They had to advance in a thin valley consisting of sodden ploughed land. Made worse by the fact that the winter ploughing was always deeper then the summer ploughing. If you've ever been to a festival you'll know what thousands of people moving across the same piece of mud will do to it. Imagine if they all have 50-60 pounds of army on, are crushed close together by the people behind and can barely see thanks to their visors. Basically, the land stops being solid. One can expect at least a good foot of mud. Imagine walking through that encumbered with 60 pounds of metal. Your not going to be in any fighting state at the end. Here the archers may have been useful. An arrow hits with one hell of a thud even if it doesn't kill you. Knights knocked down may have drowned in their armour. Others broke the cohesiveness of the line. Cavalry sent fleeing by the archers also shattered the military order of the advancing French. All this meant that when the French Men-At-Arms reached the English line they were exhausted, broken and half-blind. They were in no fit state for anything much, let alone a fight to the death (or capture).
Nevertheless, Agincourt didn't change much of anything. Henry V continued his retreat and King Charles remained King. It shocked Europe because of the sheer scale of French defeat (especially the capture of nobles) but that's about it. I'd strongly recommend doing Crécy rather then Agincourt. It defined Anglo-French relations for a hundred years.