What does Boxing Day have to do with boxing?
late 12c., from Old French fals, faus (12c., Modern French faux) "false, fake, incorrect, mistaken, treacherous, deceitful," from Latin falsus "deceived, erroneous, mistaken," past participle of fallere "deceive, disappoint," of uncertain origin (see fail).
Adopted into other Germanic languages (cf. German falsch, Dutch valsch, Danish falsk), though English is the only one in which the active sense of "deceitful" (a secondary sense in Latin) has predominated. False alarm recorded from 1570s. Related: Falsely; falseness.