The word “forest” comes from Middle English forest, from Old French forest (also forès) “forest, vast expanse covered by trees”; first introduced in English as the word for wild land set aside for hunting without the necessity in definition for the existence of trees (James 1981;Muir 2000,2008). Possibly a borrowing (probably via Frankish or Old High German) of the Medieval Latin word foresta “open wood”, foresta was first used by Carolingian scribes in the Capitularies of Charlemagne to refer specifically to the king’s royal hunting grounds. The term was not endemic to Romance languages (e.g. native words for “forest” in the Romance languages evolved out of the Latin word silva “forest, wood” (English sylvan); cf. Italian, Spanish, Portuguese selva; Romanian silvă; Old French selve); and cognates in Romance languages, such as Italian foresta, Spanish and Portuguese floresta, etc. are all ultimately borrowings of the French word.
The exact origin of Medieval Latin foresta is obscure. Some authorities claim the word derives from the Late Latin phrase forestam silvam, meaning “the outer wood”; others claim the term is a latinisation of the Frankish word *forhist “forest, wooded country”, assimilated to forestam silvam (a common practice among Frankish scribes). Frankish *forhist is attested by Old High German forst “forest”, Middle Low German vorst “forest”, Old English fyrhþ “forest, woodland, game preserve, hunting ground” (English frith), and Old Norse fýri “coniferous forest”, all of which derive from Proto-Germanic *furhísa-, *furhíþija- “a fir-wood, coniferous forest”, from Proto-Indo-European *perkwu- “a coniferous or mountain forest, wooded height”.
Source: Wikipedia page “Forest”, “Etymology” section.