Good question, but the scope is enormous. A few observations (with the hope that others will also contribute).

First, there is a problem with asking about "a medieval person." Folklore changes over time, so we can't be exactly sure about someone's traditions and beliefs from the twelfth-century - and these were likely different from those of the eighth - or the fourteenth - centuries. Not only does "medieval" cover a lot of historical turf, but it is only possible to have a limited idea about these early forms of folklore. We can answer your question with more precision when we compare fantasy and children's literature with folklore that was collected carefully beginning in the nineteenth century - and with that and by connecting dots in medieval literature, we can begin to speculate about earlier forms of tradition and belief.

With all that said, a few things seem obvious to me. One of the first things that strikes me is how a lot of literature that employs folk motifs impose a strict good-versus-evil structure onto the supernatural world. This was largely alien to the folk. For the average pre-industrial, rural resident of Britain, Faerie was extremely dangerous and had to be treated with caution and respect. A person of good character might do well in an encounter with these supernatural beings, but the supernatural beings were a fickly lot and mostly they were something to be avoided. The idea that there were good elves and other evil forces was something that would have bewildered the pre-industrial folk. That is the thing that strikes me most.

We can see something of this question in the difference that separates the elves of Tolkien's "The Hobbit" (1937) and his "The Lord of the Rings" (1954-1955). The elves in the former are whimsical and dangerous. It is unclear which side they are on because mostly they are on their own side, and it is far better not to have to deal with them. Avoidance is best. Those of "The Lord of the Rings" fall more squarely on the side of good. They are not as treacherous and dangerous as Tolkien depicted them in his earlier effort. It is my impression that fantasy literature has leaned in the direction of "The Lord of the Rings" more than "The Hobbit" - but I'm sure that there are readers here who know more than I and will gleefully inform us about how wrong I am on this score!!!

Then there is a question of unicorns: these creatures were not part of folk belief. They figure in medieval bestiaries, so it is clear that clerics knew of them and speculated about their existence in some remote place (and/or time), but the folk knew nothing of them. Fantasy literature has taken this literary motif and placed it amongst folk motifs, creating a stew that would be unfamiliar to pre-industrial folk.

The same can be said - in a different way - about giants and dragons. The folk regarded these entities as generally belonging to a remote time or place. One would expect to be able to talk with people who enountered elves in some capacity (I have talked with people in Ireland who saw a banshee or experienced the sidhe/fariesi in some way), but one would not generally find anyone who could speak in a first-person way about seeing a dragon or a giant. They were usually regarded as vanquished or extinct, long ago. It is true that the Anglo-Saxon Chronicle records references to people seeing dragons in the clouds, but it is unclear how "first-person" this record is. It is likely that the cleric recording that reference knew of it from a person, who knew it from a person, who knew it from a person, etc. Regardless of how we untangle that and other examples, most pre-industrial rural residents of Britain would only understand the presence of giants and dragons in fantasy literature as an analogy of their own folktales. This genre of oral narrative were the novels of the folk, told not as fiction. The folktales contrasted with legends, which people told to be believed. So while giants and dragons were not likely to figure in legends told about the present time, folktales often included them because they were cast in a remote time. But even in the folktales, one would not be likely to find a unicorn!