Thank you all for this interesting thread and its cross-references. As a native French speaker -and fairly well-read at that- I can assure you that the line "tenant ses tripes dans ses mains" can only refer to the king's own guts. As others have written, the very context of the song points at this interpretation.
The song is said to have ancient origins: As late as the 1950's "Rive Gauche" recordings(!) As earlye as the XIth century (when the French/Oil dialects were still in their infancy)
The über-romantique Gérard de Nerval brought this colourful, poignant, fatalistic ballad up to the attention of the French litterati and it is one of the most iconic songs for those who tried to demonstrate the antiquity of the French tradition. (The antiquity of its theme/s stands almost alone in a French traditional corpus which can generally be traced back to the early 18thC sometimes back to the 16thC).
These facts were well known when Pierre Barlatier published the collective and popular paperback Regards Neufs Sur La Chanson (ed. du Seuil, 1954).
The recently published massive -and almost definitive- Patrice Coirault catalogue (Répertoire vol.I-III, 1996-2000,etc ed. Bibliothèque Nationale de France) will help the Francophones among you answer further questions and dispell some of the myths.
As for my own contribution, I would like to point out that
1) the imagery -and therefore ethos- of the English and Scots adaptations -printed here-, excellent as they are, divert significantly from the French original(s)
2)the "argument" of the song is a lie pushed to its ultimate limits before it breaks. This device is used, to comic effect, in songs like "Seven Drunken Nights". I do not know how ancient it is but I would not be surprised if it was already known in Ancient Greece or further afield in India and beyond. A good illustration of how intractable the age of a ballad is: are we talking of the music, the formulas, the prosodic patterns, the themes, the devices? The interest? The unbroken oral heritage?
Bensusan's or Dutertre's renditions notwithstanding, to many French people who may recognise this song today it is indexic/a token of the renewed approach to chanson/singing started in the postwar (WWII) period, when authenticity and simplicity (in delivery and orchestration) became the new rallying cries of a young generation, educated about French past, both sophisticated and thrifty, warry about commercial values and wanting to break free -gently- with the more rigid aspects of traditional French mores.