Gauntlet (the glove) comes from Old French gantelet (little glove), from Frankish *want — but 'run the gauntlet' is actually from Swedish gatlopp (lane-run), a completely different word that English merged by coincidence.
A heavy armored glove; also, a challenging ordeal or series of difficulties one must face.
From Old French gantelet, the diminutive of gant (glove), from Frankish *want (glove), from Proto-Germanic *wantuz. The phrase 'throw down the gauntlet' (issue a challenge) comes from the medieval practice of throwing one's armored glove at an opponent's feet. The phrase 'run the gauntlet' is actually from a different word: Swedish gatlopp (lane