Please note, there have been a substantial number of sub-par responses to this question. There have also been a couple comment threads commenting on deleted comments, which is common, but useless, commentary.

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I've been reading a Distant Mirror: The Calamitous 14th Century by Barbara Tuchman, and other than a few members of the nobility killing their sons (eg Francesco Ordelaffi, the "tyrant of Forlì"), I haven't seen much about kings killing people with their own hands (at least, off of the field of battle and without a reasonably convincing just cause).

Ordering assassinations, however, was done. A notable example is the killing of Charles d'Espagne, Constable of France, by Charles, King of Navarre. The King of France had recently bestowed upon the Constable some lands that had been the property of the house of Navarre. Angry at the slight, Charles of Navarre hired a set of assassins led by his brother to kill the Constable. He made some half-hearted attempts to pretend it wasn't his doing, but eventually wrote in a letter to Pope Innocent VI, "God knows it was I who with the help of God had Charles d'Espagne killed". Given that the King of France immediately confiscated Navarre's Norman properties, it would seem that no one was really under any illusions about the culprit of the murder.

As for punishments, there was the confiscation of land, but it wasn't until 3 years later that Charles of Navarre and several of the assassins were seized. Charles was imprisoned (and, after being freed the next year, went on to wreak quite a bit of havoc in France). The actual assassins were executed.

The Constable was quite close to the King of France, and the fact that the King who orchestrated it mostly got off is quite telling. I wonder what his punishment would have been if the victim had been a man of lesser importance? (Speculation: this probably did happen, but simply tends not to make it into the history books.)

The example isn't quite the hands-on defenestration from the movie, but gives some insight anyway, I think.

Interestingly, the book notes that, "While total absence of inhibition was characteristic of persons born to rule, bizarre bursts of violence were becoming more frequent in these years, perhaps as a legacy of the Black Death and a sense of the insecurity of life.... In England, coroners' rolls showed manslaughter far ahead of accident as cause of death, and more often than not the offender escaped punishment by obtaining benefit of clergy through bribes or the right connections." So perhaps though the scene is inaccurate in other ways, the outburst of violence and lack of punishment isn't quite as inaccurate as it seems to our modern eyes.

[Note] I'm not a historian; I've just been reading a book that seemed to shed light on the question. I also haven't seen Braveheart, so I might be missing important context for the scene. Mods: let me know if I should change anything to improve the quality of the post.

I can provide an example. While not royalty, it was a very influential man who commited the murder.

Bo Jonsson (Grip), probably the richest and most influential non-royalty in Swedish history was only a Sven (Esquire), the lower of the two ranks of Swedish nobility at the time - the other being Riddare (Knight). He was Riskråd (member of the advisory council to the King, which at times had more power than the King) and Drots (a position akin to a Field Marshal, Supreme Commander and Seneschal/Steward on one). He was a large land owner in his own regards, but he also lent large sums of money to the crown and recieved control of (and the tax income from) about 1/3 of the arable land in medieval Sweden as a pledge for the loans he had issued.

He lead the noble revolt against King Magnus Eriksson (Bjälbo) and made sure Albrekt of Mecklenburg was installed as King of Sweden. In that process he became Drots and de facto regent of Sweden. He acquired land partially to ensure the power of the crown was permanently reduced, which might have been a factor in Sweden being included in the Kalmar Union after the death of Albrekt of Mecklenburg.

1382 Bo Jonsson (Grip) murdered his distant relative the Knight Karl Nilsson (Ferla) in Riddarhomskyrkan church! Not only did he murder a nobleman, claiming he had an affair with his wife, Margareta Pedersdotter (Porse), he did so with arms - in church. He also claimed that Karl Nilsson (Ferla) had attacked him first.

Despite killing a nobleman with a weapon, in a church, Bo Jonsson (Grip) was powerful enough to avoid any reprecussions for his act.

https://youtu.be/4S7QARslq74?t=10s is the scene OP is mentioning

As a follow up question to this, how much did the signing of the Magna Carta play into scenarios like this one?