I wrote briefly on the factors that enabled the English to win at Agincourt here. In short, you are correct in thinking that Agincourt was not such a surprise in hindsight. The English had a number of advantages (and the French had a laundry list of disadvantges) that evened the odds despite the French numerical superiority (which was not as extreme as is commonly portrayed). Many of these factors emerge primarily in hindsight. It is easy for me, as a historian in 2017, to look at Agincourt and suggest that in reality, the English had a quite good chance of winning.

However, this does not necessarily reflect the views of the participants, who would not have had as much perspective and distance from the subject as we do today. A hungry, tired English army that had been ravaged by disease outside Harfleur and engaged in a long march across France for weeks would perhaps not be so optimistic. French commanders, whose troops were well-supplied and had not been stuck in such terrible conditions for the duration of the campaign, had a thought-out battle plan and a large body of experienced soldiers they could rely on. But the reality was that a pitched battle in medieval warfare was a desperate and risky thing regardless of the tactical situation. Given the fact that a commander's only means of giving orders was either shouting or sending a man on a horse to go deliver a message, much of a battle would take place outside of anyone's direct control. Soldiers could panic from a vague rumor and take flight. A unit could get lost in fog and be away from an engagement until the battle had already been lost. A commander could be cut down in the press, forcing his troops to reevaluate their motivations for continuing to engage. Medieval commanders, who had neither the sophisticated technology of today's soldiers nor a dedicated general staff like 19th century Prussians, were keenly aware that once an engagement had begun, a great deal of the outcome would be left to chance, fate, or divine intervention. No one could be sure of victory, even in the most ideal of circumstances. Pitched battles were rare partly because they were such expensive, risky gambles to make.

In the case of Agincourt specifically, the major impact of the defeat was the sheer scale of the casualties. Huge numbers of French aristocrats and the professional fighting classes were wiped out on the field, and many important princes were taken hostage. An English army had not only taken a city and rampaged across France, but had smashed a superior force with minimal losses. The impact to French morale seems to have been quite immense. But the French were by no means defeated, and the defeat at Agincourt did not prevent French troops from continuing to fight on. Henry V had years of campaigning left before he could secure Normandy and force the French to sign a deal to his favor. Even then, he did not manage to consolidate English control over its newly won holdings, which would become increasingly hard to defend in the years following his death. The impact of Agincourt may more accurately be viewed as a highly successful English opening move in a new phase of the war that would eventually lead to major English territorial and dynastic gains, rather than a critical moment in and of itself.