film (n.) Look up film at Dictionary.com
Old English filmen "membrane, thin skin, foreskin," from West Germanic *filminjan (cognates: Old Frisian filmene "skin," Old English fell "hide"), extended from Proto-Germanic *fello(m) "animal hide," from PIE *pel- (4) "skin, hide" (cognates: Greek pella, Latin pellis "skin").

Sense of "a thin coat of something" is 1570s, extended by 1845 to the coating of chemical gel on photographic plates. By 1895 this also meant the coating plus the paper or celluloid. Hence "a motion picture" (1905); sense of "film-making as a craft or art" is from 1920.
film (v.) Look up film at Dictionary.com
c.1600, "to cover with a film or thin skin," from film (v.). Intransitive sense is from 1844. Meaning "to make a movie of" is from 1899. Related: Filmed; filming.