The word brief comes from the Latin brevis (short) that derives from the ancient Greek brahis (short).
From the same root: briefing, briefly, brevity, briefcase, briefness.
In modern Greek:
a) brahis: short
b) brahitis: shortness, brevity
c) brahino: to shorten, to cut down
brahis --> brevis --> brief
See the blog: English words of no apparent Greek origin at: http://ewonago.blogspot.com/