The idea that storytelling can be a profession requiring formal instruction (film school, MFA programs, etc.) seems to connect to Middle Age notions of professional storytelling. Though today's storytellers are probably a bit more specialized than those of the Middle Ages (they often don't tell stories while accompanying themselves on stringed instruments), they do fit a similar role, making their bread by telling stories expertly.
One way Medieval literary culture intersects with modern media culture is the interest in biopics: biographical pictures. For example, Martin Luther's life has recently been the subject of a biopic. Another is the proliferation of TV series, especially British series, that bring back sorcery and valiant heroes whose fate and destiny it is to free oppressed peoples through fabulous feats with the well-wielded sword.
Just a few days ago, I watched the most recent film version of Robin Hood (2010), starring Russell Crowe and Cate Blanchett. Of course, as a scholar of literature, it's impossible to turn off one's interpretive brain during films, and I was thinking about this question... I mean, really--why would modern audiences be so interested in tales from a time period where a decade's worth of problems may have been avoided, if only they had the power to send one text message! The middle ages are undeniably attractive to the film industry. Here's what I came up with to explain it:
1. Medieval literature glorifies the idea of true honor. Where men and women are honest, serve incorrigible leaders with utmost loyalty, and protect one another at any cost. I'm thinking also of a quote from another medieval-based film, Dragonheart (1996): "A knight is sworn to valor. His heart knows only virtue. His blade defends the helpless. His might upholds the weak. His word speaks only truth. His wrath undoes the wicked." It's a simplified moral world where the good are uncommonly heroic. In our day of complex political banter, philandering, and mistrust, the knight is extraordinarily appealing.
2. Novelty, adventure, and risk. A very small percentage of us risk our lives on a daily basis, but for people in the middle ages, everything they did was a risk. At least in the way that medieval lit portrays the time period, adventure wasn't a recreation, but a way of survival. Modern audiences like that. They want to be thrilled, and find it novel and entertaining to watch things like sword fighting, which they themselves would never be able to do.
3. Economics. Medieval times were times when the lower classes were often suffering for money. Whether it was because the royalty was trying to increase their margin of wealth or due to financial harship that went all the way to the top, it was difficult for the serfs to eek out an existence. Modern audiences who have suffered economically due to recession can understand and relate to this. They benefit from a wish fulfillment effect when they see that heroic knight (or outlaw) riding by to drop some precious gold into the cups of the poor.
I have to tell you, I read and agree with all of the above posts, but to be honest all I kept thinking as I read your question was ... Monty Python and the Holy Grail. Ha! Honestly, this film has become an absolute cult classic, ... and you pretty much can't study British Literature without at least hearing about this film which loosely (stress on "loosely") follows the story of King Arthur. It features characters such as Arthur and the Knights of the Round Table (including Sir Robin the Not-Quite-So-Brave-As-Sir-Lancelot and Sir Not-Appearing-In-This-Film) who participate in totally surreal and slapstick dark humor this time set deep within the Medieval time period although created "way back" in the year 1975. In my opinion, they are an acquired taste.
I agree with the above posts, and in addition wonder if there is a sense in which the popularity of such films as Beowulf and the Lord of the Rings Trilogy signal a desire for a return to some kind of golden age when things were not so confused and muddy as they are in today's world. One aspect of such media examples is that there are clearly defined "good" and "bad" characters, with very little confusion regarding this. Is our liking for such black and white moral universes a response to the increasinly confused world we live in today where there appear to be very few moral absolutes and where increasingly everything is turning into shades of grey?
Another area of pop culture where medieval and modern media intersect are fairs or ("faires"). There are hundreds of them in the United States. Click here for a complete list of "Renaissance, Medieval and Pirate Faires." The way the two media intertwine at these festival is, for example, the playing of ancient instruments which you can then purchase recordings of on DVD or video.
In addition, there are medieval restaurants around the United States, chiefly "Medieval Times." Here, you can witness re-enacting of jousting matches, eat medieval foods, and see authentic dress. Like the faires, you can purchases DVDs and CDs and also get your picture taken with a king, queen, or knight.
I think the most obvious place for the intersection between medieval literature and modern media culture is in the film industry. It seems with the advancement of digital media in film, it is becoming increasingly easier to realistically portray the medieval culture and folklore such as dragon slaying, larger than life castles and meade halls, and inhumane heroic acts.
Think of the more recent films like Beowulf, The Lord of the Rings Trilogy, Excalibur, Braveheart, and King Arthur. Consider that classic stories are well-liked for a reason, and with the many advancements in cinematography and special effects, and the addition of digital media, these stories can be visually updated, but remain classic.