The Collaborative International Dictionary of English v.0.48:

Amende \A`mende"\, n. [F. See Amend.]
   A pecuniary punishment or fine; a reparation or recantation.
   [1913 Webster]

   Amende honorable. (Old French Law) A species of infamous
      punishment in which the offender, being led into court
      with a rope about his neck, and a lighted torch in his
      hand, begged pardon of his God, the court, etc. In popular
      language, the phrase now denotes a public apology or
      recantation, and reparation to an injured party, for
      improper language or treatment.
      [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

AMENDE HONORABLE, English law. A penalty imposed upon a person by way of
disgrace or infamy, as a punishment for any offence, or for the purpose of
making reparation for any injury done to another, as the walking into church
in a white sheet, with a rope about the neck, and a torch in the hand, and
begging the pardon of God, or the king, or any private individual, for some
delinquency.
     2.  A punishment somewhat similar to this, and which bore the same
name, was common in France; it was abolished by the law of the 25th of
September, 1791. Merlin Rep. de Jur. h.'t.
     3. For the form of a sentence of amende horrorable, see D'Agaesseau,
Oeuvres, 43 Plaidoyer, tom. 4, p. 246.