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French word foyer comes from Latin focus, and later Latin focarius (That which concerns the hearth A kitchen-boy.)
focus (Latin)
(figuratively) house, family. Firepan, coal pan, brazier. Fireplace, hearth.
focarius (Latin)
That which concerns the hearth A kitchen-boy.
focārius (Late Latin)
*focārium (Vulgar Latin)
foyer (French)
Hearth. Home, domicile. Household. Lobby, foyer. Source, centre, seat.