Valverde began his professional career at Girondins de Bordeaux. After the departure of second-choice keeper Frédéric Roux, Valverde was given the #1 shirt and was set to serve as understudy to French international Ulrich Ramé. While Roux was at the club, Valverde made only two league appearances in three years.L´Equipe Career stats Bordeaux won the Coupe de la Ligue in 2007, but Ramé started and Valverde was left on the bench. However two years later Bordeaux won the Coupe de la Ligue again but this time roles were reversed; Valverde played and Ramé was left on the bench. He also made 12 appearances as Bordeaux won the 2008–09 Ligue 1 title. On 24 July 2009, Valverde joined recently promoted club US Boulogne.Dépêche – Boulogne : Valverde à l’essai On 9 December, due to numerous injuries suffered by their goalkeepers, Toulouse FC acquired Valverde from Boulogne.
