Basically it was a few factors that won Agincourt for the English,
1.The battlefield narrowed towards the English line, making it extremely difficult to keep the proper charge of knee-to-knee, and also somewhat diffused the French advantage in numbers.
2.It had been raining heavily the night before, and this made the ground extremely muddy. Horses would of had great difficulty in galloping through the mud (not as bad as the Germans in Russia, but pretty close). Once the Knights were unhorsed by the Archers, they'd have great difficulty getting up anyway, and with sticky mud clingling to them it would be even more difficult.
3.The French Knights still thought that one good charge would bring them the day. They knew how deadly the Longbow was against them, but they charged anyway. Also, the Knights were not a coherant disciplined fighting force like the English were. They ignored their leader, Charles d'Albert, and this was their undoing. They were easily stung into battle by a single flight of arrows.
4.The French knights and men-at-arms were tightly packed into "battles" 40 men deep. This limited their manouverability drasticly. Also, if just one horse was killed it could easily start a chain reaction, tripping all of the other horses and completly destroying any cohesion the unit once had.
5.The Longbow and the Longbowman were pivotal in the battle. The Longbow seriously demoralised the French and the Archers, able to quickly move in and swarm the stranded French knights, could easily kill thousands of their heavily armed opponents. Also, the use of wooden stakes in front of the Archers helped immensly against cavalry.
6.Henry V, although his speech before the battle probably wasn't quite as dramatic as Shakespeare's, was reported to be at the frontline of nearly all the fighting. This would of given the English a huge morale boost, whereas the French king, Charles VI was nowhere to be seen.
7.The English had their own reserve of fresh Knights which they sent around the back and the flank of the French army. This is what broke the already confused French.