If you must place LOTR in some kind of historical period (and you shouldn't), it will have to be the eighteenth century, around the start of the industrialisation.

Saruman tears down the forests around Isengard to fuel the industry which equips his army. As Treebeard says:

Down on the borders they are felling trees - good trees. Some of the trees they just cut down and leave to rot - orc-mischief that; but most are hewn up and carried off to feed the fires of Orthanc. There is always smoke rising from Isengard these days.

Furthermore, when the hobbits return to the Shire, they find that Lotho "The Chief" has transformed the Shire:

Worse, there was a whole line of the ugly new houses all along Pool Side, where the Hobbiton Road ran close to the bank. An avenue of trees had stood there. They were all gone. And looking with dismay up the road towards Bag End they saw a tall chimney of brick in the distance. It was pouring out black smoke in the evening air.

The inns in the book also don't really fit mediaeval inns, but are more like eighteenth century ones.

So you're probably best off thinking of Middle Earth as an idealised pre-industrial society without gunpowder, which is starting to get ruined by greed and industry. There isn't much mediaeval about that.

Medieval life is not depicted by these books. They are not even inaccurate depictions, they are simply not depictions of medieval times. They are inspired by some tropes/associations we have to medieval times, nothing more. A point-by-point list of inaccuracies would thus be a pretty monumental task, and frankly I have trouble figuring out where even to begin. Maybe you could make your question more specific? Like, are you more interested in agriculture/economy/everyday life/social mores/religious beliefs/warfare etc.?

These books are part of the established Northern Thing in heroic fantasy, so your question is about their resemblance to Northern Western Europe, not China, not Mesopotamia, not Italy, not Antiquity or the Renaissance. (Lin Carter, Imaginary Worlds)

Hobbits have clocks, calling cards, and umbrellas, not to mention glass in all their windows and pots of tea. They are very modern.

The Rohirrim are supposed to be based on the Anglo-Saxons (their names are) but I know of no sedentary but horse-focused culture with magnificent steeds. Gaulish horses generally ran to inbred ungainliness, and they were often trying to bring in fresh studs. (Piggot) The early Franks in the Altfeld might have been a bit like this, or early Goths in the same area, but that's late antiquity, not medieval (Sulimirski, The Sarmatians)

We don't get to see much of cultures. The characters are usually in the wilderness. The books you mention are notable for being cultures totally without religion, which seems very non-European and non-Medieval. Religion only appeared in the Silmarillion, and then there's a creation myth but no sense of religious practice.

In short, medievalesque but not historical with magic added.