Where does “фоаје//foaje” come from?

фоаје//foaje (Serbo-Croatian) comes from French foyer, from Vulgar Latin focarium, from Latin focārius, from Latin -ārius, from Proto-Italic *-āzios — Forms relational adjectives to nouns (and rarely numerals).

Ancestry of “фоаје//foaje”, step by step

Step	Language	Word	Meaning
1	French	foyer	hearth; lobby, foyer; home, domicile
2	Vulgar Latin	focarium	—
3	Latin	focārius	a kitchen-boy
4	Latin	-ārius	er
5	Proto-Italic	*-āzios	Forms relational adjectives to nouns (and rarely numerals)

Every word from Proto-Italic *-āzios →Every word from Latin -ārius →Every word from Latin focārius →