When an adjective owes its origins to a proper noun, it should probably be capitalized.

Thus we write about Christian music, French fries, the English Parliament, the Ming Dynasty.

Some periods of time have taken on the status of proper adjectives: the Nixon era, a Renaissance/Romantic/Victorian poet (but a contemporary novelist and medieval writer).

Directional and seasonal adjectives are not capitalized unless they're part of a title:

We took the Northern route during the spring thaw. We stayed there until the town's annual Autumn Festival of Small Appliances.