The Collaborative International Dictionary of English v.0.48:

Courant \Cou*rant"\ (k??-r?nt"), a. [F., p. pr. of courir to
   run, L. currere. Cf. Current.] (Her.)
   Represented as running; -- said of a beast borne in a coat of
   arms.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Courant \Cou*rant"\ (k??-r?nt"), n. [F. courante, fr. courant,
   p. pr.]
   1. A piece of music in triple time; also, a lively dance; a
      coranto.
      [1913 Webster]

   2. A circulating gazette of news; a newspaper.
      [1913 Webster]