So first of all, I want to clarify a couple things here--the Hundred Years' War had actually been raging for quite some time at this point, with most historians putting the starting date in 1337, and the events of "The King" taking place in and around 1415, the year of the Battle of Agincourt. Now, in the context of the movie, Henry V believes that an assassin has been sent to attempt his murder, but what he discovers in his conversation with his wife, Catherine of Valois, Charles VI's daughter and the sister of the Dauphin so memorably portrayed by Robert Pattinson, is that there was no French-ordered assassin. Charles, suffering from bouts of mental illness and resultant domestic strife, isn't particularly interested in re-igniting war with the English at this point, and in Catherine's opinion, her brother is a little too stupid and frivolous to organize such a thing. So what does Henry do with this information? He confronts Gascoigne, his Chief Justice, realizes that he must have been behind the plot because of how much he benefited from the victory at Agincourt in terms of money and land, and proceeds to stab him to death in the same scene.

As to whether this is what actually happened in history: in a word, no. First of all, there's no evidence to suggest Gascoigne's murder, and he didn't hold office long into Henry V's reign (whether this was due to Henry dismissing him or his own voluntary resignation, given that he would have been in his 60s at that point, is unclear). Similarly, there's no evidence to suggest that Gascoigne made any attempt to drive Henry into war, and I'm not aware of any assassination plot, sent by the French or otherwise, that Henry faced directly before invading France (surely, if there had been one, you'd think he would have utilized it for propaganda purposes), save for the Southampton plot, which was decidedly domestic, since it involved other English nobles attempting to depose him in favor of his second-cousin-once-removed, Edmund Mortimer (this plot is portrayed briefly in "The King" as well). In reality, Henry didn't need much of a push to start up war with France again, and the English nobility didn't need much convincing, either. Edward III had claimed at the beginning of the war that the true right to rule France ran through his line due to his mother's place in the French royal family, and between the instability in France resulting from Charles VI's mental illness and Henry V's desire to assert his own vulnerable dynasty (since, as Catherine points out in "The King," his own father had usurped the throne from his cousin), the timing couldn't have been better.