Where does “fumaige” come from?

fumaige (Old French) comes from Latin fumus, from Proto-Italic fūmos, from Proto-Indo-European dʰuh₂mós, from Proto-Indo-European dʰewh₂- — smoke; mist, haze.

Ancestry of “fumaige”, step by step

Step	Language	Word	Meaning
1	Latin	fumus	smoke, steam; indication, sign
2	Proto-Italic	fūmos	smoke
3	Proto-Indo-European	dʰuh₂mós	smoke
4	Proto-Indo-European	dʰewh₂-	smoke; mist, haze

Every word from Proto-Indo-European dʰewh₂- →Every word from Proto-Indo-European dʰuh₂mós →Every word from Proto-Italic fūmos →