The English word "fair" in the sense of a large yearly market derives from Classical Latin feriae, meaning a holy day (Holy Day). This evolved into Medieval Latin feria, a market fair, then into Old French as feire.
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"Fair" in English actually has two origins. The noun, meaning "a gathering for entertainment or public sale," is from Latin feriae "holidays, religious festivals" (always plural). The adjective, originally meaning "pleasant, beautiful" with extended meanings "light-skinned" and "free from bias," is a native English word from Proto-Germanic *fagraz (the asterisk indicates a reconstructed form).
As a side note, feriae is also the source of the Portuguese weekday names, segunda-feira for Monday, terça-feira for Tuesday, quarta-feira for Wednesday, quinta-feira for Thursday, and sexta-feira for Friday. These are derived from medieval Catholic designations of the days of Easter Week: "second holiday" and so on.