A hotel would be nothing; you could call on anybody at a hotel, if you had to; but here would be a demarche indeed!
1650s, "walk, step," from French démarche (15c.) literally "gait, walk, bearing," from démarcher (12c.) "to march," from de- + marcher (see march (v.)). Meaning "a diplomatic step" attested from 1670s. A word never quite anglicized.