NB: I have yet to do any serious scholarly investigation on this subject; right now, I’m concentrating on working out my own ideas and reasoning.
It seems to me that a lot of scholars who specialize in medieval literature also end up working with fantasy, both as creative writers and as scholars. For example, J.R.R. Tolkien was a professor of medieval literature at Oxford, and he wrote (among other scholarly things) a book on Beowulf. Although I haven’t looked for it, I know from other scholars that Tolkien ‘borrowed’ extensively from Beowulf and other medieval literature in his creation of the Lord of the Rings series and its companion works. Perhaps lesser known, but no less important in some ways, Kathryn Hume first wrote a scholarly book on The Owl and the Nightingale. She later went on to write another scholarly work on fantasy literature, Fantasy and Mimesis. One of the founders of the Monty Python comedy troop, Terry Jones, has written several books on Chaucer.
Clearly, you don’t need to be a medievalist as an academic specialty to create good fantasy literature. The late great Terry Pratchett includes medieval elements in his Discworld series, but he himself once said, his learning was broad, not deep. Patrick Rothfuss was an English major who went to graduate school, but I have no idea what he may have specialized in or if he took an advanced degree (his website says “I don’t’ want to talk about it.”). If I had to speculate, if not a specialty, Rothfuss has at least done some in depth study of medieval literature and/or history. There’s too many accurate parallels between medieval realities and the world of The Kingkiller Chronicles to be coincidence. Then again, maybe I’m overanalyzing.
Similarly, successful fantasy does not need to be terribly medieval or academically based. Take The Elfstones of Shannara by Terry Brooks. This book has a lot of classic high fantasy elements like the unwilling hero, the journey, the band of friends, the elves and humans, the magic, demonic bad guys, etc. The world is generically medieval but there’s not much detail about the world itself; that’s not really the point of this series. It’s more about the characters and the plot. I have to admit, I only read the one and half of the novels, but I could already tell that there was a pattern, and I got bored.
Fantasy also doesn’t need to be medievally-based at all. V.E. Schwab’s A Darker Shade of Magic and its sequels hints at some research into the history and culture of Renaissance and Victorian England, but that’s not medieval. Likewise, Naomi Novik’s Temeraire dragon series is built on historically accurate life during the Napoleonic Wars in the early 19th century.
Then there’s fantasy that’s built on mythologies, which often places them in somewhat medieval times or settings. Again turning to Naomi Novik, Uprooted is clearly based on Eastern European folklore; the Baba Yaga references give that away, as do some of the character names (I’d never heard of the names Agnieszka and Kasia until I met my Polish now aunt). The general time and place have a medieval feel, although not nearly as detailed as the likes of Tolkien and Rothfuss. I love Uprooted for many reasons, but it’s not as detailed in the same way.
Then there’s the fantasy that is based on myth but set at least partially in the modern world. For example, there’s Neil Gaiman’s adult novels, including Anansi Boys and American Gods, which are heavily based in African and Norse mythology respectively, though not exclusively. Then there’s the YA versions, most notably Rick Riordan’s series Percy Jackson for the Greek myths, and Magnus Chase for the Norse.
Eventually I’m going to need to get into the actual scholarship done on these questions, but for now I think it’s safe to at least say that modern fantasy literature has a serious debt to medieval literature and culture and probably history too.