OED: Etymology: Probably a merging of two words of distinct origins:
(i) shortened < demean n.;
(ii) a loan < Middle French, French mine countenance, facial expression (13th cent. in Old French in phrase faire mines to grimace, make faces), appearance, manner, air (late 15th cent.), probably < Breton min muzzle (see below).
I heed the Etymological Fallacy, but is the English spelling of mien strange or startling? If it's shortened or derived from 'demean' (as OED says above), would 'mean' be more natural?
For example, modern French still retains the spelling « mine » to mean 'appearance, look'.