Old English framian "to profit, be helpful, avail, benefit," from fram "active, vigorous, bold," originally "going forward," from fram "forward; from" (see from).
Influenced by related Old English fremman "help forward, promote, further, do, perform, accomplish," and by Old Norse fremja "to further, execute." Sense focused in Middle English from "make ready" (mid-13c.) to "prepare timber for building" (late 14c.). Meaning "compose, devise" is first attested 1540s.
The criminal slang sense of "blame an innocent person" (1920s) is probably from earlier sense of "plot in secret" (1900), perhaps ultimately from meaning "fabricate a story with evil intent," first attested 1510s. Related: Framed; framing.