Hernandez's goal in the 64th minute was backed with a penalty kick score by Cuauhtemoc Blanco in the 79th minute while Mexican goalkeeper Oscar Perez came away with the shutout.
The victory pulled Mexico into a tie with Uruguay, which defeated South Africa 3-0 Wednesday, for the lead in Group A with four points. France and South Africa trail with one point each.
Round-robin play finishes Tuesday for Group A when Mexico plays Uruguay, a game in which a tie sends both teams to the second stage, and France goes against South Africa.
France and Mexico played even most of the match but a long pass found Hernandez -- he was nearly offside -- breaking free midway through the second half. That left him one-on-one with French goalkeeper Hugo Lloris. Lloris came out to meet Hernandez but missed on a foot-first tackle, giving Hernandez an easy shot for the goal.
Gerardo Torrado was tackled by Eric Abidal while moving in on goal by, a ploy that gave Mexico a penalty kick. Blanco kept the ball low to the left side, just out of Lloris's reach for the sealing score.