From Latin 'fames' (hunger) — entered English during the repeated food crises of the late fourteenth century.
Extreme scarcity of food in a region, causing widespread hunger and death.
From Old French 'famine,' from Vulgar Latin *famīna, from Latin 'famēs' (hunger). Latin 'famēs' is of uncertain deeper etymology, though some scholars connect it to a PIE root. The word entered English during a period of recurrent famine in medieval Europe, replacing the native Old English term 'hungor' (hunger) for the concept
In Italian, 'fame' means 'hunger' — from the same Latin 'famēs.' If you say 'ho fame' in Italian, you are saying 'I have hunger' (I'm hungry), using a word that in English means something completely different. English 'fame' (renown) comes from Latin 'fāma' (rumour, reputation), a completely different word — one of those false-friend traps that delights linguists and torments