early 14c., controve, contreve, "to invent, devise, plan;" late 14c., "to manage by a plan or scheme," from Old French controver (Modern French controuver) "to find out, contrive, imagine," from Late Latin contropare "to compare" (via a figure of speech), from an assimilated form of Latin com "with, together" (see con-) + tropus "song, musical mode," from Greek tropos "figure of speech" (from PIE root *trep- "to turn").
Sense evolution (in French) was from "invent with ingenuity" to "invent falsely." Spelling in English was altered by the same unexplained 15c. sound change that also affected briar, friar, choir. Related: Contrived; contriving.