The word medieval should never be capitalised unless it begins a sentence or forms part of a title. The term the Middle Ages should always be capitalised, except for the the. Occasionally you will find that older writers capitalise medieval.

Why is medieval not capitalised?

The OED records "medieval" as both adjective and noun, though in neither instance is the word "medieval" capitalised, except where it appears at the start of a sentence. Hence I would adjudge that it is not a proper noun, and hence it should not be capitalised.

Does medieval Europe need to be capitalized?

Capitalization, "medieval" and "Middle Ages" - As a rule, "medieval" is not capitalized when used adjectivally (e.g., medieval Europe ), although some editorial styles allow for it.