Tobacco, potatoes, and a bunch of other items were unknown to medieval Europeans, and they feel (to me) out of place in medieval fantasy as well (setting aside the fact that Tolkien insisted LotR was set in Europe in our world).
But Lord of the Rings wasn't set in the middle ages, nor was it really in Europe, though he went back and forth between stating that the Shire was in Northwestern Euope at about the same latitude as Oxford around 6000 years before the present. But he also said things that implied his "
Middle Earth" was mythological as well, but he never attempted to tie it in strongly with the real world in terms of Geography or anything.
The theatre of my tale is this earth, the one in which we now live, but the historical period is imaginary. The essentials of that abiding place are all there (at any rate for inhabitants of N.W. Europe), so naturally it feels familiar, even if a little glorified by enchantment of distance in time.(Letters, no. 183)
I take this to mean that it's a fantasy set in a world that is based on our own, but with a lot of creative license taken.
Tolkien borrowed heavily from some the languages and mythology of Northern Europe, obviously. The "
Merry England" archetype figured heavily into his Shire, certainly, while his Rohirrim resembled Saxons, and his dwarves were rather Norse, and Gondor seemed more like a classical civilization.
Many of the comfortable archetypes we're familiar with from D and D style "medieval" fantasy is more Renaissance, or even 18th century, than Medieval. There are a number of myths and misconceptions about the real middle ages as well (like the notion that no one ever bathed, or that most girls were married by their early teens, or that people were sexual prudes back then--Evidently, no one ever read Chaucer).
There's no rule that a fantasy novel's setting
has to be completely consistent or faithful to the middle ages, in any case. Unless one is creating a historical fantasy that is set in the real world during a specific time. Even then. things like the presence of magic, or the existence of fantasy beings could change the dynamics of a society a lot.
Not saying that you shouldn't do that if you think it would be fun. And I think it's always handy to research things so you can get a sense of what's plausible or possible in a given setting. But one thing to consider also is that the middle ages took place over almost a thousand years, and there were many changes that occurred throughout. The world of 1100 is going to be very different than the 1400s, and of course a society modeled after, say, one of the Italian city states will be very different from one modeled on England or Germany..