I'm going to try to unite the different angles here of "what they knew historically" and "within Arthuriana," because I think OP's question is trying to get at both. :)

I love this question! I just finished an answer on whether medieval Christians knew that Christianity and Islam were related, but we don't usually talk about what Christians knew about Islam historically.

"Saracen" and its equivalents (in Middle German it's haidin/heiden...you do you, Middle German) started off as words connoting geographic origin, unrelated to religion. "People associated with Sarah" is a false etymology. But by the time Arthuriana was popular in the West--12th century--it pretty much just meant "Muslim."

If late medieval western Europeans knew one thing about the beliefs of the Saracens--whether they saw it as idolatry, heresy, or a false religion--it was the association with Muhammad. There are some literary examples that turn Muhammad into one third of a demonic "un-Trinity" to turn Islam into an antichristianity. But by the late Middle Ages, there was also a thriving market for stories about Muhammad the false prophet. You might know, for example, that Dante sticks him in the eighth circle of the Inferno, with the heretics.

And believe it or not, one of the most popular 'literary' texts in the late Middle Ages, in its full version, has a Life of Muhammad smack in the middle of it. In other words: a text that situates the foundation of Islam historically.

The Golden Legend by Jacobus de Voragine (13th century) is this sprawling collection of saints' lives and legends from the span of Christian history more or less to that point. It gets translated from Latin into all the vernaculars; it gets excerpted and anthologized and plagiarized and re-anthologized. Bourgeois parents use its stories to entertain their kids at night and priests use its stories to entertain their audiences during sermons.

And why not? These are some great stories. St. Katherine of Alexandria single-handedly debates fifty pagan philosophers in intellectual combat. St. Margaret of Antioch gets eaten by a dragon...and then bursts out of its stomach, alive. Take that, Jurassic Park.

And for whatever Earthly reason, Jacobus stuck a passage from the History of the Lombards right into the section where he's talking about St. Pelagius. Ahen in the middle of THAT random insert, he stuck his version of the nasty, polemical, Life of Mahomet.

As as the transition between excerpts goes:

And when Gregory was dead Sabine succeeded after him, and to him succeeded Boniface the third, and to him Boniface the fourth, at whose request Phocas the emperor gave to the church of Christ the temple of Pantheon, about the year of our Lord six hundred and ten.

And he, at the request of the third Boniface, established the See of Rome to be chief and head of all the church. For tofore, the church of Constantinople wrote herself greatest of all other churches. And when Phocas was dead Heraclius reigned.

And about the year of our Lord six hundred and ten Mahomet the false prophet, and an enchanter, deceived the Hagarenes or Ishmaelites, that is to say the Saracens, in this manner as it is read in a history of him in a certain chronicle.

So here we are: in one of the most popular literary (non-used-for-Church-ritual-or-administrative-life) books of the late Middle Ages, a pretty flat-out statement that gives a year for the foundation of the Islam. And it's a date well after the historical dates linked with Arthur in English sources.

Of course, just because the story is in the full Legenda doesn't mean any one person had access to a particular legend (even a very literate and wealthy person, as the authors of Arthurian stories were). Medieval text circulation didn't really work that way, especially not for a full text as expansive as the Legenda. And I'm not holding my breath that Wolfram von Eschenbach or Thomas Malory was sitting on a copy of the Annales Cambriae that gives a date for the Battle of Mount Badon.

Educated medieval people--again, this is who we're talking about with the composers of Arthurian material--absolutely had the chance to know when Islam was historically founded.

But when it comes to Arthuriana, the overwhelming message is that historical accuracy was less important than emotional resonance. Arthur exists in his own weird fantasy space. Okay, you're laughing because this is so immediately obvious; you didn't have to read this far to learn THAT. Arthur, the person, is essentially a fantastical figure. Even 15th century English people were twigging to that.

But also true? English Arthurian writers in particular use "the Saracens" as one of their main strategies to drive home the emotional, dare I saw nationalist importance of Arthur to their audiences. In later English translations of French Arthuriana, "the Saxons" get replaced by "the Saracens." And Malory, of course, takes up this charge for his now-famous, originally-English version. "The Saxons" no longer meant anything as a threat to readers--so they simply wouldn't do as a threat for Arthur to face.