Although Harfleur was nothing to sneeze at, it wasn't exactly the kind of prize that would be sufficient to justify the massive expenditure of the campaign so far. The English army, although they had plenty of guns for the siege of Harfleur itself, decided to leave its guns at Harfleur for the defense of the conquered city. This indicates that they had no real intention of embarking on any other sieges deeper into the heart of France. So what was Henry trying to accomplish? Many sources disagree. One chronicle, which is not particularly accurate about the campaign in general, asserts that Henry had to go to Calais because his original navy had been scuttled by a storm. However, a more accurate account seems to have been given by Jean Le Fevre, a French herald who was actually embedded with the English army on its march from Calais. He says that Henry "wanted a battle." The French commanders opposing Henry also were quite aware of his intentions: "they knew well that, even from the moment he left his own kingdom, his desire was to give battle to the French." The dukes of Orleans and Bourbon seem to have attempted to schedule a battle with Henry, but he rejected their proposals. Henry essentially told the French to come at me, bro: "there was no need to appoint a time or a place because they could find him any day they liked in open country and without any hindrance." Henry was unlikely to be able to succeed in another major siege effort like that of Harfleur (which had taken a very long time and had exacted a serious toll on his forces). If he went deeper into France while dragging around a siege train with heavy guns, the French would have found it much easier to attack him at a time and place of their choosing. With a lighter, more mobile force that was almost entirely mounted, Henry could raid all the way to Calais and more effectively pick his ground for a field engagement. Contrary to many popular assumptions about the battle of Agincourt, the English army was not a rag-tag band of peasants heroically making a stand against a vastly larger and superior foe. Henry's army, like the French, was primarily made up of experienced professional soldiers.

The French did outnumber the English, but not by more than a few thousand. In addition, the English had a major advantage in terms of cohesion and command. Their army had been marching and fighting together as a single entity since the campaign began. The French forces were still assembling even on the day of the battle, causing great confusion. The French captains and officers were not the arrogant and foolhardy bravos of Shakespeare's play, but experienced soldiers (some of whom were older and had more experience in battle than Henry V). However, there was no doubt in the English ranks where the chain of command ended; Henry alone made the final call on important decisions. Once he had decided, there was no arguing with him. His swift and heavy punishment for those accused of involvement with the Southhampton Plot before the army embarked would have left no doubt in the minds of his captains about his enforcement of discipline. The seniors officers of the French, by contrast, were good soldiers but without a single overall commander who was clearly and explicitly in charge of the others. Although they formed clear and intelligent battle plans before Agincourt, they were unable to properly carry these plans out owing to the confusion and chaos within their ranks. Henry had to have been aware of many of the advantages he possessed, because he seems to have had fairly good information on the activities of the French via capturing prisoners. Agincourt, like all pitched battles, was a risky and dangerous proposition, but it wasn't as much of a long shot for Henry as is often portrayed.

Hiya!! So you have gotten one excellent answer, and I just wanted to add more political context as to why Henry V was counselled against the Calais march as well as the French position during this campaign.

To begin with, the English memories of previous French campaigns were not exactly fond ones. The Hundred Years' War, or how we refer to it now, had begun well for the Plantagenets. Edward III had continental allies in Flanders and Brittany, and his victories at Crecy and Poitiers had been devastating for the French Kings and their supporters. The English mounted chevaunchees nearly unopposed, and revolts broke out as the French Crown struggled to maintain any semblance of functioning government, even at a fundamental "Protector of the Realm" type of level.

This changed with the ascension of Charles V of France. Charles V worked to weaken Edward III and the Prince of Wales (who was ruling in Aquitane). He focused on restoring the basic functionality of government, particularly the taxation infrastructure, and diplomatically isolating Edward III from his allies. He slowly but steadily built up the royal finances, so he would be able to better utilize France's inherit advantage in resources. He was able to turn the Breton War of Succession into a pyrrhic victory for the English, as he recognized the new Duke of Brittany, who in turn paid homage to him as overlord. He organized and deployed the notorious mercenary companies that raided the French countryside to Castille to back Henry of Trastamara in the civil war, which won him yet another ally when Henry triumphed, and restored some basic stability in the country. The Castillan Civil War also bankrupted the Black Prince, who was forced to raise taxes in Aquitane, whose nobility revolted and requested Charles V's aid, restarting the war.

However, unlike Edward III's earlier campaigns, this one was more of struggle. The French reverted to the Fabian strategy and refused to give battle to the English unless they held a decisive tactical advantage. Unlike previous French campaigns that relied heavily on pitched battle, the French army thinned itself out and relied on their heavy fortifications to overextend the English and then harry them throughout the country. Charles V himself was a very sickly man and was content to remain behind his fortifications; I can't really find any major campaigns that he personally led after becoming king (it is worth noting that his father, John II, had been captured by the English at Poitiers, and died in captivity). Instead he paid to assemble disciplined, experienced soldiers under the command of Bertrand du Guesclin, the new Constable of France. As u/MI13 noted, command structure is important here, while Charles V was not personally in the field, the level of trust he placed in Guesclin (he had ransomed du Guesclin multiple times from capture) and other captains were well-known, and while he was not in the field, the fact that these officers held the confidence of the King gave them considerable authority, even if they were not of high birth. This will become important later!

The result was disastrous for the English, as many of the hard won gains of Edward III's long reign were wiped away in little over a decade. Both Edward and the Prince of Wales were physically unable to lead campaigns at this point, and the taxes required for a now losing war effort were widely unpopular, helping to contribute to the Peasant's Revolt and Wat Tyler's uprising. As the French drove the English back to a few key port cities on the continent, and began raids of the English coast, the war position became increasingly untenable. Eventually, as both countries were plagued by the instability of minor Kings and regencies, a peace was agreed to which heavily favored the ascendant French.

So keep in mind that this was the environment in which Henry V was proposing his campaign. Not only was his own position somewhat insecure due to the fact that his father had usurped the throne from Richard II, but it would have appeared to many observers that he was mimicking the strategy that had failed several decades earlier: paying for expensive professional soldiers to raid France between English-held towns (also expensive to maintain), risking disease and attrition to bait the French into attacking him, hoping that his freedom of movement would destabilize the French government and nobility. However, simply capturing Harfleur would not do to maintain support for the war at home. Even after Agincourt and his incredibly successful Normandy campaign, parliament was still reluctant to award Henry V taxes for his war and he had to fund much of it through his newly acquired French lands. This is part of Henry's motivation, to maintain his position in the aristocratic politics of the day by looking to engage the French in battle. But this is not without risk, as there is no guarantee that this type of campaign will be successful.

So we've covered the English, so what about the French? Well Charles V had died fairly young, leaving a regency for his young son Charles VI. This was not a terribly stable period, but Charles VI managed to make it through to adulthood and negotiate a favorable settlement with the English. However, he then began to experience the first of many psychotic episodes, which would debilitate him and the French government. A regency was assumed by his uncles, but over the course of his long reign, this had developed into an internal power struggle at the French court, between the King's cousin and his brother. When his cousin, the Duke of Burgundy, murdered his brother, this turned into an outright civil war, known as the Armagnac-Burgundian war. So not only do you have issues of corruption and ineffectiveness that accompany many medieval administrations, but you have powerful noblemen at each others throats, while nominally all serving France. And at the top of it all, the King is mad and unable to effectively address any of these problems.

I say this because cohesion and command structure have already been mentioned, so I just want to reiterate how important they are. Charles V did not personally lead many of the campaigns that had driven the English back a few decades before. But in most other senses, he was a "strong" king, able to create effective government structures, manage aristocratic politics/diplomacy, and effectively deputize subordinates. The French of 1415 were already infighting, with partisans who wanted to give battle and those who didn't both vying for the favor and position in the regency. Indeed, it was the intervention of the Duke of Berry, one of the oldest nobles in the country who attempted to play peacemaker between these faction, that ensured that the King and the Dauphin were not present at Agincourt, as Berry remembered the chaos that had followed the capture of his father at Poitiers. Therefore, as the army arrays for battle and makes decisions, cohesion will break down as groups of soldiers follow the commands of the men who lead them, rather than having a single commander, king or otherwise, making decisions.

Hopefully this has helped shed some context on why Henry V wanted to march to Calais, why his counsellors may not have wanted him to, and the composition of French leadership at the time. Let me know if this helps and if you have follow ups/want reading material!!