When it was me by Paula Deanda is probably the song you're looking for! This song opens with the line: "She's got green eyes and she's 5'5". Long brown hair all down her back".
Songs that mention girls with brown hair Paula Deanda's track, When it was me, is available to view on YouTube, so you can easily listen to it and check whether this is the song you're looking for.
Long Brown Hair by Regina Spektor is another song you may want to investigate, and Della's Long Brown Hair by Amazing Rhythm Aces also mentions a woman with brown locks.
Finding songs about girls with brown hair and green eyes If none of these are exactly the song that you were after, then I'd recommend taking a look at one of the many internet lyric-searching tools available.
