None of the Fool's occult identity is medieval, and the layers can be dated with some precision.
In 1781 Antoine Court de Gebelin published, in the eighth volume of his Monde primitif, the claim that the tarot preserved a book of Egyptian priests. In the same volume the Comte de Mellet supplied the other half of the apparatus, matching the twenty-one trumps and the Fool to the twenty-two letters of the Hebrew alphabet. Both essays are wrong about history. Both were enormously influential, and very nearly everything esoteric written about the tarot since descends from that one publication.
Eliphas Levi turned the correspondence into a working system in Dogme et Rituel de la Haute Magie, issued in two parts between 1854 and 1856, and it is his arrangement that first binds the trumps to the paths of the Tree of Life. Levi did not put the Fool at the head of the sequence. He placed him near the end, between Judgement and the World, on the letter Shin. The now-standard assignment, Fool, Aleph, the element Air, the eleventh path running from Kether to Chokmah, comes instead from the Hermetic Order of the Golden Dawn, founded in London in 1887 and 1888, and reached a wide public only through the decks and books its former members produced. Waite prints the Fool as 0 and then discusses him out of sequence anyway; Crowley keeps the Golden Dawn placement and defends it at length.
A modern account of this card therefore stacks four layers roughly a century apart: a fifteenth-century game piece, a 1781 Egyptian fantasy, an 1850s Kabbalistic scheme, and an 1890s revision of that scheme. Each is worth knowing. None is the others, and presenting the whole stack as one ancient tradition is the most persistent error in tarot writing.