Costil started his career at SM Caen in Ligue 1 but only made a 10 performances for the club before being sent on loan in the 2008/2009 season to Vannes Olympique Club in Ligue 2. On 17 June 2009 CS Sedan signed Costil from SM Caen until June 2011. Then he played two years for Sedan making 76 appearances. He was elected best goalkeeper of Ligue 2 for the season 2010/2011. On 14 June 2011 he signed a 3-year contract for Rennes after his contract with Sedan expired. This transfer means he returns to Ligue 1 for the first time since the handful of appearances he made at Caen at the beginning of his career.