Wordorigins.org

How did a word meaning a bundle of sticks become an epithet for a gay man? It was process of gradual semantic shift over several centuries and continents.

The ultimate origin of faggot, the word for a bundle of sticks, is unknown. The English word comes from the French fagot. There is an apparent cognate in the Italian fagotto, so there may be some common Latin root. But if so, it has been lost. From Cursor Mundi, a Northumbrian poem from before 1300:

Gong ysaac a fagett broght.
(Isaac came bringing a faggot.)