Cuoq won the French Gravel Rally Championship in 2005, 2006, 2007 and 2010. In 2007 he also won the French asphalt title, but in February 2008 he was stripped of this title for having a notebook from the previous year during the reconnaissance for the Rallye du Var.[1] He and co-driver David Marty also had their licenses suspended for 24 months, with 12 months suspended.
In January 2007 Cuoq made his World Rally Championship debut on Monte Carlo Rally where he finished ninth. One year later he scored his first WRC points by finishing seventh.
After his suspension he returned to the WRC for the 2010 Rally de Portugal, but retired from the rally.