Where does “false” come from?

false (Middle English) comes from Old English fals, from Latin falsus, from Latin fallō, from Proto-Indo-European ǵʰwel- — to bend; to lie, deceive.

Ancestry of “false”, step by step

Step	Language	Word	Meaning
1	Old English	fals	falsehood, fraud, counterfeit; false
2	Latin	falsus	deceived, tricked, cheated, disappointed, having...
3	Latin	fallō	—
4	Proto-Indo-European	ǵʰwel-	to bend; to lie, deceive

false — Etymology, Origin & Word History | Etymology Explorer