This would be incorrect. For one thing, Europe was pretty crowded during the Middle Ages, even though its population wasn't as large as today. For another, there is a lot of technology in Tolkien's world which wasn't present in the Middle Ages, and vice versa.

The Shire was the most populous region of Eriador, but there is no indication they used anything but post-Medieval farming techniques. Gondor, on the other hand, seems to have preserved a classical civilization (which is why many people compare it to the Byzantine empire, which was able to maintain large standing armies for centuries after the system collapsed in western Europe).

Rohan's people lived mostly in the valleys of the Ered Nimrais, and there are several indications they were farmers, but there is strong debate over whether the Riders of Rohan were full-time professionals supported by a farming population or semi-professional soldiers who mostly served in time of war, or in yearly rotation to keep their skills fresh.

The Elves of Lorien, Lindon, and Eriador clearly had agricultural skills and techniques which were superior to those of the hobbits, because Sam Gamgee (a gardner by profession) was extremely impressed with their produce and foods.

The Dwarves didn't even grow their own food. They relied solely upong trade for their supplies. You won't find any cultures in Medieval Europe like that.

Middle-earth was a mixture of peoples and cultures, and Tolkien used more than one model to create his world. He also freely intermixed elements from different times and regions.
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