The next season, Baguette moved to both Eurocup Formula Renault 2.0 and French Formula Renault 2.0 championships with Epsilon Euskadi. He finished eighth (tied on points with seventh Junior Strous) in the European championship and eleventh in the French one, including a second place at Pau. He continued in both series in 2006 with a fourth place overall in the Eurocup, including five podiums and a win at Le Mans, finishing just 11 points behind championship winner Filipe Albuquerque. He finished in eighth in the French championship, again for Epsilon Euskadi.