Why is not there no gender - neutral reference for someone from England or France,

As was mentioned before language doesn’t have to be consistent. The difference between calling someone from Korea ‘a Korean’ and someone from France ‘a French’ is simply that the former is standard English, and the latter isn’t English at all. There doesn’t have to be any other reason, just like there’s not for all kinds of variations in virtually all languages. But as a practical matter I dispute there’s almost ever any real confusion caused by referring to a person from Korea as ‘a Korean’.

After thinking very hard about it, I actually have read - not actually heard spoken, but read - “a Vietnamese” in writing about the Vietnam War. I’ve never heard it in reference to other “-ese” groups.

Oh, apropos of nothing, someone from Monaco is called Monegasque. Not an ethnicity that many Americans will ever have occasion to discuss, since perhaps 5% of them even know what or where Monaco is.

The Shakespeare quote is not an example of “French” or “English” being used as a singular noun. If it were, it would be “a dozen Frenches” and not “a dozen French”.

I know where Monaco is. Are you French?

Both are perfectly normal here in the UK.