1) French word used in English 
• (p. pr.) A circulating gazette of news; a newspaper. • (p. pr.) A piece of music in triple time; also, a lively dance; a coranto. • (a.) Represented as running; -- said of a beast borne in a coat of arms.
Cou·rant' adjective [ French, present participle of courir to run, Latin currere . Confer Current .] (Her.) Represented as running; -- said of a beast borne in a coat of arms. Cou·rant' noun [ French courante , from courant , present participle ] 1. A piece of music in triple time; also, a lively dance; a coranto. 2. A circulating gazette of news; a newspaper. 
In heraldry, courant describes an animal when running.
(of an animal) represented in the act of running: a greyhound courant.