If he is fuming, he is smoking — literally. And it is, subtly, the same word in Spanish.
“To fume” comes from the Latin root fumus (“smoke”) from which we also get the common Spanish word for “smoke”, humo. But they don’t sound alike, so how are they related?
The Spanish humo is a great example of the pattern of the Initial F turning into an H in Spanish, alone among the languages of the world. Many Latin words that began with an F that came to us in English through the Latinate F form, became the equivalent word but with an H- in Spanish. Take hermano and filial, for example. Or fact and hecho.
Other English words from the same root fumus include fumigation (ahhhh!) and the less common fetid. Fetid is a dirty, Shakespearean word, after all.