OK, this one took some digging. First, this did not ring true with any reference to women's clothing of the period that I'm familiar with. It's fairly well known by clothing historians that clothing of both sexes around the time of the Black Death had become more tailored (the fashion is sometimes termed the "cote-hardie", or "garment for the brave", because of this trend), but there is certainly no evidence of garments for women that were so short they showed their "arses and private parts." Men, on the other hand....absolutely. There are plenty of depictions and descriptions of extremely short cotes for men, and since they wore hosen laced into these garments or suspended from a belt, usually over linen braies, their "arses and private parts" would indeed be visible (or at least silhouetted or suggested) through the thinner linen worn for underclothing. So I had a hunch to follow.

I found the reference in Frankopan, referring to short hoods and a garment called a paltok. Frankopan cites the Chronicle of John of Reading through Rosemary Horrox's collection of translated sources on the Black Death. Notably, Horrox's translation refers only to "the English", not to women. Through Horrox I was able to track down the original Latin source, Chronica Johannis de Reading et Anonymi Cantuariensis, where I searched for the unusual term "paltok". The Latin edition and my search terms can be found at https://archive.org/details/chronicajohannis00taituoft/page/n8/mode/2up?q=paltok

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**Page -348-**P. 167, 1. II. Alienigenarum insaniae indumentorum varietate semper adhaerens. This denunciation of the eccentricities of men's dress about 1365 should be compared with the more general description of the fashions of a time twenty years earlier, given in the preceding continuation of the Westminster chronicle (above p 88), and with the violent attack upon the articles of male attire singled out by Reading, which is introduced into the Eulogium (pp. 230-1) under the year 1362 After describing the new supertunic, called a ' Gown,' which viewed from the back made the wearer look more like a woman than a man, a novelty unnoticed by Reading, the monk of Malmesbury inveighs, as he does and in very similar terms, against the small hoods buttoned tightly under the chin {modo mulierum) with a long streamer behind falling to the heels, the doublet and the tight hose of motley (paltok and caligae) and the 'beaked' or piked shoes which were known as ' crakowes.' He alone mentions the gold and silver girdles worn by many who could ill-afford such extravagance, but, on the other hand, says nothing of the long daggers dangling between their legs and the caps shaped like hose or sleeves, with which Reading concludes his enumeration of the perversities of contemporary fashion.

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**Page -349-**P. 167, 1. 13. Caputiis parvulis. It seems to be implied that these hoods were so small that they were not drawn over the head for protection against sun and rain, but, like their surviving representative the academic hood, merely covered the shoulders. The ' tipet ' or, as it was more generally termed, the ' liripipe,' was a prolongation of the baj; of the hood in the shape of a cord or streamer, which fell down the back sometimes to the heels. When the hood was drawn over the liead, the tippet was sometimess wound round the upper part, to get it out of tlie way. It was so worn by Siinkin in the Reeve's Tale (Chaucer's Works, ed. Skeat, IV, 1- 3.953)

P. 167, 1. 15. 1Paltoks . . . caligis. The 'Paltok' was a short jacket of silk or woollen cloth which did not reach the loins, and was attached to the closely-litting hose (caligae) by latchets or points, which in derision of the character of the wearers were popularly called harlots, gadlings or loiels (losels), all of which were current words for a worthless idle fellow, a rascal (see the glossaries to Skeafs editions of Piers the Plowman and Chaucer; a different application of 'gadling' in its secondary sense is found in Baker, p. 113). The derivation of 'Paltok' is discussed in the New Eng. Dict., s.v. Paltock, and in Way's note to the word in the Promptorium Parvulorum (Camden Soc), p. 3S0.

This is the Latin passage from p. 167.

Pracvcnit et sequebatur pestilentia non praevisa; nam plurimi lectos suos ingrediebantur sani, et subito exspirabant. Morbillae, quae Anglice dicuntur " Pokkes," diversa hominum et animalium inficiebant genera et inter- ficiebant. Adhuc et ventus ille zephyrus, qui tribus annis praeelapsis fortia multa contrivit, in capite Decembris monasterium Radyngi cum vicinis locis horribihter laceravit; ibique diabolus in specie deformi apparuit. Nec mirum ; levitas enim Anglorum ahenigenarum insaniae indumentorum varietate semper adhaerens, nec futura propter hoc praevidens mala, caputiis parvulis, quae scapulas tegere valebant, laqueatis cum ahs botenatis mento strictissime, tipettatis ad modum cordarum, insuper Paltoks aliis vestibus curtissimis lanis ac aliis tenuis obturatis ac consutis per totum, quae anos suos seu verenda celare nequiverunt, caligis etiam tibiis longioribus ad curta vestimenta colligulatis ligulis quas harlotes, gadelinges et lorels vocabant, sotularibus quoque lateraliter rostratis, ac cultellis longis inter tibias dependentibus, atque capellis panneis retortis ad formam caHgarum seu manicarum aptatis, uti coeperunt. Quorum deformitates et stricturae non Deo vel sanctis, dominis suis nec sibi invicem genuflectere, servire aut revereri absque grandi miseria sinebant; quamplures | etiam in conflictu hostili pericliari cogentes.

The tl/dr here is that this passage definitely refers to men's clothing. What may have thrown off Frankopan was the reference to "harlotes", which was, as explained in the text, a derisive term applied to the men who wore these fashions. He might have also just assumed that any reference to scandalous clothing must have applied to women. But it is clear from the original Latin source that this passage is referring to men.

The super-short tl;dr answer is that Frankopan misunderstood the source to be talking about women when it's talking about men. (And I see that's already been answered but I started typing this last night and I won't stop now!)

Stella Mary Newton actually addresses the same quote Frankopan refers to in her book, Fashion in the Age of the Black Prince, in the context of discussing the great changes occurring in western European dress in the fourteenth century. To give a basic description of these changes, I'll quote myself from an earlier answer:

This is actually quite an interesting period in fashion history. At the outset of the century, men's and women's clothing (cottes or cotes) appears to have been rather loose and unshaped; the tailoring techniques we take for granted, like set-in sleeves, weren't in use, and neither were the lacing or fastenings needed to make a tight bodice able to be put on and off. This is "before fashion", when dressing to impress meant making use of the best and most expensive fabrics in lavish lengths, rather than conforming to the newest cut or construction. This type of clothing is fairly easy to sew - the pieces are generally rectangles with minor modifications, which is also economical and results in little wasted fabric. Here are two thirteenth-century stained glass windows at the Cloisters that show what I'm talking about - King Louis IX and Woman Dispensing Poison; as you can see, the basic gown of men's and women's clothing isn't really gendered. You would generally find more differences in other aspects of dress, like hairstyle/headgear, or slight differences in skirt length.

By the middle of the century, however, we're in what's sometimes called the "tailoring revolution". The shaped sleeve and armscye allowed a closer fit in the shoulder and upper arm, while buttons and lacing down the front or sides allowed the bodice to close in on a defined waist. This was rather wasteful of fabric, since more dramatic shaping to the pieces meant that they wouldn't fit together smoothly on the flat fabric, and therefore more scraps would be generated. We also start to see changes in cut and fit that indicate differences in social status and fashionability. The most fitted garment, worn directly over the body linen, was the cotte/cote, often layered with a slightly less well-fitting surcote (by definition), and a mantle/cloak/outer wrap could be worn as well. [...] And at the same time, the houppelande was introduced - a voluminous, excessive, sometimes fur-lined garment to be worn with a belt over the fitted clothing, generally with sleeves that were either gathered at shoulder and wrist or else slashed open and worn trailing. In either case, it was a sumptuous display of wealth and style.

Following the English victory at the Battle of Poitiers in 1356, the royal family and English nobility were flush with cash from French concessions and ransoms. This gave them greater means to show off with new fashions taken to even more extreme lengths. As you can see in the above broad description of the changes, the major important point about this new style was that it showed off the body, which had not been done before. Commentators like John of Reading, the author whose quote Frankopan uses, were aghast. Men were wearing upper body garments that were short enough to show the tops of their hose! Wearing hoods tight against their throats! But there were other types of excess that horrified them as well. Jeweled liripipes! Gold and silver belts! Shoes with long pointed toes! Fashion at this time was very much coming from the top down and clothing like this - even beyond the gold and jewels - was simply not worn outside of court circles.

Newton looks into what information we have of paltoks to try to figure out what distinguished them from other garments. She finds that they were worn only by men, and they appear to have been padded and lined and, judging from the amount of thread required to make them, likely quilted. According to John, they had no front opening, and the particolored hose (which Newton translates as having been called "harlots" as a derogatory nickname, rather than the men wearing them being referred to as harlots/harlot-like for wearing them) was laced to them at the waist, a method of holding top and bottom garments together that would become very common in following centuries.