The "other" OED has it coming from German, Branny: haversack
1749, from Fr. havresac (1680), from Low Ger. hafersach "cavalry trooper's bag for horse provender," lit. "oat sack," from the Gmc. word for "oat" (cf. O.N. hafri, M.Du. havere, O.H.G. habaro). "Haver is a common word in the northern countries for oats." [Johnson]
Online Etymology Dictionary