The term itself comes from an old Saxon term meaning ‘fear’
This is incorrect
The Norman rulers of England introduced the word as a legal term, as seen in Latin texts such as the Magna Carta, to denote uncultivated land that was legally designated for hunting by feudal nobility (see Royal Forest).
Before that the word appears to have originated in French
The word forest derives from the Old French forest (also forès), denoting "forest, vast expanse covered by trees"; forest was first introduced into English as the word denoting wild land set aside for hunting without the necessity in definition of having trees on the land.
The precise origin of Medieval Latin foresta is obscure. Some authorities claim the word derives from the Late Latin phrase forestam silvam, denoting "the outer wood" with forestam meaning "outer" or "outside" a proscribed boundary such as property line.