Webster's Revised Unabridged Dictionary · 1913

Demure

Demure (de*mūr") , adjective

[Perh. from Old French de murs (that is, de bonnes murs of good manners); de of + murs, mours, meurs, mors, French mours, from Latin mores (sing. mos) manners, morals (see Moral); or more prob. from Old French meur, French mûr mature, ripe (see Mature) in a phrase preceded by de, as de mûre conduite of mature conduct.]

1.
Of sober or serious mien; composed and decorous in bearing; of modest look; staid; grave.
Sober, steadfast, and demure. — Milton
Nan was very much delighted in her demure way, and that delight showed itself in her face and in her clear bright eyes. — W. Black
2.
Affectedly modest, decorous, or serious; making a show of gravity.
A cat lay, and looked so demure, as if there had been neither life nor soul in her. — L'Estrange
Miss Lizzy, I have no doubt, would be as demure and coquettish, as if ten winters more had gone over her head. — Miss Mitford

Demure , intransitive verb

To look demurely. [Obsolete] — Shakespeare