Midfielder Kossoko benefited from a bad clearance to find the back of the net 17 minutes from time after Nancy's Samba Diakite, who was sent off with 10 minutes left, had cancelled out Anthony Le Tallec's 50th-minute opener following a splendid solo run.
Elsewhere, Jeremie Aliadiere netted a double as a second-half substitute to give Lorient a 3-2 victory at Ligue 2 side Guingamp after extra time.
Former Arsenal and Middlesbrough striker Aliadiere netted on the 84th and 113th minutes from close range as Lorient recovered from 1-0 down.
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