The Collaborative International Dictionary of English v.0.48:

Outrance \Ou`trance"\ ([=oo]`tr[aum]Ns"), n. [F. See
   Outr['e].]
   The utmost or last extremity.
   [1913 Webster]

   Combat a outrance, a fight to the end, or to the death.

   Syn: fight to the finish.
        [1913 Webster]