Moreau began his motorsport career in 1995 in karting, where he was active until 2001. In 2002, the young gun in the French Formula Renault, in which he finished in twelfth place overall at the end of the season. He also participated in a race of the Formula Renault 2.0 Euro Cups in part. 2003 remained Moreau in the French Formula Renault and he improved with four podium finishes in fourth place in the drivers' standings. He also began again at some races in the Eurocup, where he finished 17th overall in this season. 2004 Moreau denied his third season in the French Formula Renault and succeeded with three wins to reach the third place overall. He also improved in the Eurocup, although he remained winless, to seventh place in the overall standings.
2005 joined the French in the Formula 3 Euro Series. With a win in Zandvoort, he finished at the end of the season eighth place overall. In 2006, he remained in the Formula 3 Euro Series, however, he had this year with a second place settle for the best result and tenth place in the overall standings. He was, inter alia, his teammates and later Formula 1 driver Romain Grosjean behind. 2007 Moreau left the Euro series and he went to the World Series by Renault for KTR at the start. In the new series, he chose a race for himself and took the end of the season 14th overall. He also was the year of his debut in the Le Mans Series and the 24 Hours of Le Mans. 2008 Moreau stayed with KTR in the World Series by Renault. However, it was replaced after five race weekends by Sergei Afanasyev. Nevertheless, he finished at the end of the season in the standings to 16th place. His successor Afanasyev was without points in last place in the drivers' standings. In addition, Moreau launched again in the Le Mans Series, where he won the championship title with Patrice Goueslard, and he took part in the 24- hour race at Le Mans. 2009 Moreau returned to the fifth race weekend in the World Series by Renault back. With a third place as best result he finished at the end of the season 18th overall. In addition another launch in the 24- hour race in Le Mans he took part in two races in the FIA GT Championship.