From Medieval Latin brūnus "brown, brunet" (whence also Spanish bruno, French brun, Dalmatian broin), from Frankish *brūn, from Proto-Germanic *brūnaz (“brown”), from Proto-Indo-European *bʰerH- (“shining, brown”).
Akin to Old Dutch brūn "brown" (Dutch bruin "brown"), Old High German brūn "brown" (German braun "brown"), Old English brūn "brown". More at brown.