Lord of the Rings, at least, isn't even _trying_ to be medieval, is it? Like, the shire seems vaguely 18th/19th century England, Gondor seems suspiciously Roman/Byzantine... I don't think Tolkien was going for "this is [whatever period], only with dragons", and even if he was, that period certainly wasn't medieval.
Middle-earth arose from Tolkien's early attempts to reconstruct English / Anglo-Saxon mythology. Apart from the anachronistic Shire, the world largely feels early medieval.
