The Les Mis link is fascinating - it's hard to see how "Petite Paternotre blanche" could be a mishearing of "with pater noster" or "witches' Paternoster"!

Here's a footnote from William A. Wheeler (ed.) (1878), _Mother Goose's melodies; or, songs for the nursery_.

Matthew, Mark, Luke, and John. A charm formerly much used by children instead of a prayer. There are many variations of it. See for a number of such, taken down from the lips of children in the dioceses of Worcester and Salisbury, a "Report on the state of parochial education in the Diocese of Worcester," by the Rev. E. Field, printed as an appendix to the National Society's report for 1841. Ady, in his "Candle in the Dark," London, 1656, p. 58, gives the first two lines as having been used in the time of Queen Mary.

The origin of the lines is perhaps to be found in the "Enchiridion Leonis Papae," first published at Rome in 1532, and early translated into French. This work consists of a collection of prayers, for the most part burlesqued or disfigured and adopted as charms to avert
or heal diseases. One of them, entitled "Paternotre blanche, pour aller infailliblement en paradis," contains this sentence: "Au soir m'allant coucher, je trouvis trois Anges a mon lit couche's, un aux pieds, deux au chevet, la bonne Vierge Marie au milieu," etc.

So there you go - it all comes from the 16th-century Handbook of the Lion of the Pope. Perfectly straightforward.

Or is it? Did the Enchiridion Leonis Papae even exist? Here (again courtesy of Google) is a footnote from an edition of the Canterbury Tales:

Carrington (1879) cites several contemporaneous versions of the Petite Paternotre Blanche in French and Provencal. One of the latter (p. 129) has a conclusion in which the Blessed Virgin "tells whosoever recites it, to have no fear of the dog or wolf, or wandering storm, or running water, or shining fire, or any evil folk." There are other versions in German, Italian, and Spanish. All are variants of the "Now I lay me down to sleep" theme.

Skeat ( 1894:5.106) cites an example from the "(apocryphal) Enchiridion Leonis Papae (Romae, MDCLX): Petite Patenotre Blanche, que Dieu fit, que Dieu dit, que Dieu mit en Paradis. Au soir m allant coucher, je trouvis trois anges a mon lit, couches, un aux pieds, deux au chevet, etc." ("Little White Pater Noster, what God does, what God says, what God sends to Paradise. At night, going to bed, I found three angels by my bed, lying down, one at my feet, two at my head, etc.") Skeat then quotes this example, which illustrates that English versions are often nonsensical: "White Paternoster, Saint Peter's brother,/ What hast thou i' th' t'other hand.^ Heven-Yate Keyes. / Open Heaven-Yates, and steike [shut] Hell- Yates. / And let every crysome-child [Christian child] creepe to its owne mother. / White Paternoster! Amen."
...
Donaldson (1958, following Skeat and Robinson) has the most concise explanation ". . . the White Lord's prayer: this personification was considered a powerful beneficent spirit." We can conclude that Chaucer has John allude to a half-superstitious, childish prayer.