The historical accuracy of Ridley Scott's The Kingdom of Heaven has been ripped to shreds here and elsewhere for the past decade. So please, I'm not looking for anything beyond this detail:
In the opening of the movie, Orlando Bloom's wife is being buried. Before they fill up her grave, the priest or whatever orders the grave digger to sever her head because she committed suicide.
I've done some serious Google-fu but can't find anything. I see that Augustine's City of God argued that suicide was a mortal sin. And that in 1533 (according to Wikipedia) suicides were denied a Christian burial. (And then Wikipedia says, "In 1562, all suicides were punished in this way.").
So I guess my question could be extended into: would a 12th Century suicide be punished with burial outside a Christian burial ground (based on this 1533 date)? And where does this decapitation idea come from?
As OP correctly surmises, there are two issues at play here. First, the denial of a Christian burial, and second, the integrity of the body itself.
To the first: yes, people who committed suicide were denied a Christian burial (denied the honor of burial; profane burial; burial outside the Church are terms that somewhat commonly appear) as a matter of course in medieval Latin Europe. The earliest reference to this practice that Alexander Murray cites is Gregory of Tours in 570: a count who had stabbed himself was taken to a monastery but "not put among the Christian dead, and no Mass was sung for him."
Gregory helpfully points out the two crucial aspects of Christian burial: the funeral rite to be performed and the consecrated ground for the grave itself. By the later Middle Ages, a third thorny question surely planted itself in the minds and hearts of survivors. Praying for the dead was central to later medieval religion (not unimportant in earlier monasticism, either), but prayers on behalf of those in hell were considered futile.
The common location for burial of people who committed suicide and others who died outside the Church/society in some was varied over time and especially from place to place. Open fields was fairly typical in medieval France and Germany, at least in prescriptive sources (law codes). In France, there are specific references to the use of fields typically engaged for jousting and melee tournaments. Sometimes the bodies of people who committed suicide were buried along with executed criminals at the town gallows site; otherwise the waste dump might be used.
Burial of suicide victims at a crossroads hits lots of spooky Halloweeny vibes. This practice is quite richly attested in England from the sixteenth century onwards, but there is at least one reference from medieval Silesia (which was mainly German then; modern day mostly-Poland) and one Italian source that mentions burial alongside public roads. Where geography permitted it, as in parts of Scandinavia, the boundary between beach and solid ground was often used. (Calling anthropologists to discuss "liminality," stat...) And if geography, or I suppose hydrography indicated, sometimes people threw the bodies into rivers, alone or in a barrel.
The second issue relates to mutilation of bodies of people who committed suicide. While the evidence leaves some room for ambiguity, it seems on the whole to suggest that a woman who committed suicide in 12th century France, as in the movie, would not be decapitated post mortem.
Medieval corpses of the holy and the hated alike could be preserved intact or divided in all sorts of ways for all sorts of reasons. Saints' bones could become valuable relics, or the perfectly preserved body of a (typically female) saint was enduring proof of her sanctity. Heretics were frequently burned at the stake and their bodies destroyed to ash, the smallest possible particles; drawing and quartering following hanging was used only in extreme cases because the severance of the criminal body recapitulated the destruction of the civic body in high treason.
Highly ritualized mutilation as indicated by decapitation and burial between the legs is usually linked by medievalists to a pervasive phenomenon in medieval Europe: fear of the waking dead. Both decapitation and staking through the heart are richly attested in accounts by and about the early Middle Ages. With a catch: they never refer to suicides. In fact, sometimes these methods of burial are mentioned alongside a list of possible justifications for it, such as mothers who died in childbirth or unbaptized infants--but suicide victims are included in different instructions, suggesting those practices did not (normatively) apply to them.
There is one 9th century theologian who refers to the ancient, pagan practice of mutilating the corpse of someone who commits suicide by chopping off its hand. Christian of Stavelot is trying to assert what a grievous crime suicide is (by way of commenting on Judas), so Murray argues it's quite revealing that his best example is ancient and just a hand, not contemporary.
By the fourteenth century, the occasional reference to "mutilation" of the body of someone who commits suicide pops up, but it isn't clear what this entails. It's really from the later 15th century onward, especially in England and Germany, that decapitation and staking (or total destruction, as with burning) seem to have taken hold as necessary steps in dealing with the body of someone who committed suicide. The earliest descriptive reference that Murray found is from 1470s Italy. The shifting (but still tragic) attitude towards suicide in the early modern era is traced in MacDonald and Murphy, Sleepless Souls: Suicide in Early Modern England.
It's important to mention, of course, that a lot of our evidence on these questions comes from law codes (civil and canon/Church). It's clear from other sources that the prescriptive norms were not always descriptive. A group in 1283 Dunstable, England, for example, rescued their friend's body from the village dung heap and buried it themselves. While this isn't a case of suicide, individual Church elite could seize prerogative as well. Near the end of her life, Hildegard of Bingen brought down an interdict on her illustrious monastery for burying in consecrated ground on convent property the body of someone the archbishop had thought died out of communion with the Church. The efforts that medieval people would go to to camouflage suspected (or obvious) suicide of their friends and family in order to secure Christian burial suggests that there might have been some room to look the other way.
That said, a ritualized practice like decapitation and placing the head beneath the legs doesn't quite fit the same category of "flexibility between norm and praxis" as fudging how a body was found or the likely cause of death. While it can't be ruled out that the bodies of people who committed suicide might have been decapitated in 12th century France, it doesn't really fit the trends in the sources. Burning starts to become more prominent from the 13th century onward, and only after that does less disintegrated mutilation become an observed and noted phenomenon.
Further Reading: