Did the medieval Europe have an active "lowbrow" culture?

1. The question has sense for certain culture only. Islamic civilization or Chinese one were different. We are speaking only about Christian European culture, from Rus at the East to Ireland in the West and Islamic Cordoba/Granada excluded.

2. The aristocracy was not better educated these days, save military education. Only clergy had better education and looked upon traditions of other population as sinful and primitive ones. Or, in the case of higher culture of somebody of Islamic culture, it was declared for bad, foreign, non-christian or blasphemous. But you are interested in aristocracy-peasantry difference, don't you?

3. Different cultures on different social levels happen in places where two cultures met, but haven't mixed, due to the limited time or principal differences.

Such places were:

Southern France - mixed Islamic and Christian culture has already appeared as Albigense culture. It covered all layers of society.

England - there the cultures of Norman aristocracy and gentry and Saxon peasantry was different and many times described by well known writers. These cultures were not so much different, and Normans were from the same source, but they had got additional traditions in France, and automatically started to despise games of their ancestors as such of low level. It was just during the set time interval.

Eastern and Northern Europe - there the culture of higher classes was more Christian and lower classes - more pagan. And as a result, every difference was declared as pagan and prosecuted. (most often it really WAS pagan)

AFAIK, the other areas were rather monolithic in the sense of culture.

My professional historian girlfriend says,

Canterbury Tales – c.1395

Decameron – completed by 1353, Florence (though I’m fuzzy on the stories, it doesn’t have the reputation that say, the Wife Of Bath story in Canterbury Tales does)

Snowball fights, just google “medieval snowball fight” for images, largely late 14th and early 15th century

Farts and butts are not uncommon in marginalia, just as one will see cats, rabbit demons, and other things that might surprise a modern viewer (as with gargoyles, though I’m less clear when silly ones came about)

The madrigal with the chickens I mentioned last night is mid-1500s.

There is a trend here of things picking up in the mid-late 14th century, which is later than the 1300 that the OP described. Part of this has to do with the surviving material culture. But consider that Chaucer is known to have “borrowed” his tales, simply putting his stamp on the framework and stories common at the time – some known to have been told for generations. Nuns and priests as (often comically) raunchy individuals is an especially common theme, and perhaps inevitable any time you have a “chaste” class.

Might look into the European (particularly Italian and French, but also English) custom of charivari. Basically a public mob display of disapproval, not humorous per se, but sometimes using coarse humor to drive home claims of cuckoldry and such. There’s a variation that’s basically a wedding march, with the crowd “escorting” the couple home and ensuring they end up in bed with each other, then partying outside. I’m sure that wasn’t exactly a model of propriety.

Google search on “medieval pratfall” got me this intriguing bit, seems to be a whole chapter on physical comedy:

Subsequent discussion led us to consider comedia del arte - note " A special characteristic of commedia dell'arte are the lazzi. A lazzo is a joke or "something foolish" or "witty".[10][9]". Although comedia del arte is later than OP's period, note that:

Although commedia dell'arte flourished in Italy during the Mannerist period, there has been a long-standing tradition of trying to establish historical antecedents in antiquity. While we can detect formal similarities between the commedia dell'arte and earlier theatrical traditions, there is no way to establish certainty of origin.[15] Some date the origins to the period of the Roman Republic (Plautine types) or the Empire (Atellan Farces). The Atellan Farces of the Roman Empire featured crude "types" wearing masks with grossly exaggerated features and an improvised plot.[16]

We'd both be willing to be that there is an (undocumented) continuous tradition from Rome to the height of Comedia - which means that it would be present in OP's period, and providing lowbrow lazzo.

It's hard to find something that is truly lowbrow from the Middle Ages. That's because recording things in writing was expensive and done by the clergy or people financed by the elite, who would presumably much rather spend their money on the high arts.

Despite that, I know of something that I think kind of meets your criteria and has been recorded: in the literary tradition of Galician-Portuguese troubadours, there is a genre known as cantigas de escárnio e maldizer (literally "songs of mockery and badmouthing", with some authors making a distinction between cantigas de escárnio and cantigas de maldizer). These existed alongside cantigas de louvor (religious), cantigas de amigo (romantic love from a woman's perspective) and cantigas de amor (romantic love from a man's perspective).

Here's a snippet of a cantiga de escárnio e maldizer by XIII century troubadour Joan Garcia de Guilhade, with my rough translation:

Ai dona fea! foste-vos queixar / que vos nunca louv'en meu trobar; / mais ora quero fazer un cantar / en que vos loarei toda via; / e vedes como vos quero loar: / dona fea, velha e sandia!

Oh, ugly lady, you complained / that I never praise you in my singing; / but now I want to write a song / in which I will constantly praise you; / and see how I want to praise you: / ugly old crazy lady!