All right, I'll try to answer this. Some disclaimer, though.

I have NOT watched the movie. Only heard and read about it. I therefore may overlook some circumstances and point of view that might be developed in the film.

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Now let's get into it. From what I've read, the event you refer to is supposed to take place on the verge of the Battle of Agincourt, where an overconfident Dauphin comes to taunt Henry V and all. If this is so, the first thing that would prevent Henry V from outright killing the Dauphin is historical accuracy. The Dauphin was NOT at the battle of Agincourt. He was not on the field, nor near it. The French had learnt at a high cost not to send kings or heirs on the battlefield by that time, since Jean le Bon was captured at Poitiers (1356).

Now, let's assume that the Dauphin is here and taking part in the battle that ensues. That is historical fiction, of course, but could still be plausible.

The first, obvious answer, is that you can't kill an emissary, no matter how insulting he is, or nearly. If that emissary happens to be the heir of the throne of France, that makes him even more untouchable. Killing him would have been seen as utterly disloyal, cruel, unchivalric, barbaric, you name it. Relations among the nobility and between reigning families were codified and one could not break such an elemental and important rule with no consequences.

First consequence could have been severe disapprobation from Henry V own men. It is very likely that his knights, dukes, earls and all would have heavily frowned upon such a vile action.

If you take one "similar" event, the assassination of duke of Burgundy Jean sans Peur (John the Fearless) by king-to-be Charles VII at Montereau in 1419, you can see that in Charles VII own partisans the dissensions are extreme on that point. Some of his closest advisors pray him to abandon his project when they hear about it, not only because of political repercussion, but because that is such a vile deed that it would soil his honor^(1). And you've got to keep in mind that Jean sans Peur had, some years earlier, assassinated his own nephew, cousin to Charles VII. So in a way he "deserved" it, but there were still mortal enemies to Jean sans Peur that considered that assassinating him at a meeting was horrible. Now try and justify to your peers that you assassinated someone as important as the heir to the throne of France for bad mouthing you.

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Second reason would be that Henry V would keep his own survival in mind. As I elaborated here, you had no obligation to grant your prisoners mercy for their life. Now, if we see it from Henry's point of view, he's in a desperate position, caught up by a mightier French force, with his army exhausted by forced march and battered by dysentery. He expects to lose the battle, the odds are too much against him. Even wasn't expecting to lose, he knew that there was a great chance of it happening. His defeat would mean, most likely, capture for himself and a great deal of his men. Now, how do you think their captors would have reacted when they found out the Dauphin was slain in an embassy ? Killing him would certainly have meant death some people, and harsher ransom conditions for the others (especially for him).

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Finally, not directly answering your question, yet linked to it in a way, the film has been bashed a little bit in France, especially for the way it presents the French and English respectively.

From what I have read or listened to, the movie is largely inspired by Shakespeare's Henry V. And that is a huge problem, in my mind, since it is not unknown that Shakespeare's play is not quite historically accurate.

His depiction of both Henry on one side and the French knights on the other are terrible. The warmongering, butcher-like (he had all French prisoners massacred on the very battlefield, killing thousands) side of Henry V is totally overlooked, with only the chivalric king side apparent.

On the other hand, the French are generally depicted as show-off, overconfident, taunting and rather stupid militarily speaking. There might be a part of truth in that, and one could not say that French knights were not proud, yet it was far from what Shakespeare described. But talking about the representation of the Battle of Agincourt is another whole topic.

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^(1) On this subject, I recommend AUTRAND, Françoise, Charles VI. La folie du roi, Paris, Fayard, 1986.