faggot (n.1)

late 13c., "bundle of twigs bound up," also fagald, faggald, from Old French fagot "bundle of sticks" (13c.), of uncertain origin, probably from Italian fagotto "bundle of sticks," diminutive of Vulgar Latin *facus, from Latin fascis "bundle of wood" (see fasces). But another theory traces the Vulgar Latin word to Greek phakelos "bundle," which is probably Pre-Greek.

Especially used for burning heretics (emblematic of this from 1550s), so that phrase fire and faggot was used to indicate "punishment of a heretic." Heretics who recanted were required to wear an embroidered figure of a faggot on the sleeve as an emblem and reminder of what they deserved.

https://www.etymonline.com/word/faggot