> Both “French” and “British” are acceptable demonyms

No they are not.

The Oxford English Dictionary, for example makes it quite clear re. 'French':

    "With plural agreement, and frequently with 'the' French people regarded collectively ..."

I draw your attention to the first three words ... "with plural agreement".

It is explicitly telling you that "French" is a collective plural noun and hence cannot be used as a singular countable noun.