The French head into their final Group A match with South Africa knowing that even a victory might not be enough as Mexico and Uruguay can both progress if they share a draw.
Mexico controlled the first half and took the lead after the break when new Manchester United striker Hernandez beat the offside trap to score.
Blanco scored a second from the penalty spot after Eric Abidal tripped Pablo Barrera in the area.
Under-fire France coach Raymond Domenech recalled Chelsea winger Florent Malouda but the change had little effect as they struggled once again in the opening period.
Mexico continued to enhance their reputation for attacking football and should have taken the lead when Rafael Marquez clipped over the top for Carlos Vela only for the Arsenal youngster to shoot wide.
The impressive Mexican full-back Carlos Salcido got forward at every opportunity and picked out Guillermo Franco but the former West Ham striker failed to hit the target.
Salcido drilled wide from just outside the area and also forced a save from France goalkeeper Hugo Lloris after skipping past Bacary Sagna.
After Vela limped off, with what looked like a hamstring injury, Lloris punched Salcido's cross off substitute Pablo Barrera and was lucky to see the ball drop wide.
Giovani Dos Santos also drilled wide before Nicolas Anelka finally had a shot on target for France just before the interval.
Anelka was replaced by Andre-Pierre Gignac at the break and the French soon threatened through Malouda.
The midfielder burst forward and hit a powerful shot that was tipped over by goalkeeper Oscar Perez.
Franck Ribery also had a low effort pushed away at the near post by Perez as France began to pose problems.
But just after the hour, Mexico took a fully-deserved lead through Hernandez.
Marquez knocked the ball through and Hernandez broke away from Abidal, slipped around Lloris and tapped into an empty net.
Gignac attempted to get France back in the game but hit a shot well over the bar from long range.
And Mexico killed the game with 11 minutes remaining when Eric Abidal hauled Barrera down in the area.
Blanco, who is 37 and plays in the Mexican second division, made no mistake from the spot and there was no way back for the abject French.
France (4-2-3-1): Lloris; Sagna, Gallas, Abidal, Evra; Toulalan, Diaby; Govou (Valbeuna 69), Ribery, Malouda; Anelka (Gignac 46)
Subs (not used): Mandana, Reveillere, Planus, Squillaci, Clichy, Gourcuff, Diarra, Cisse, Henry
Mexico (4-3-3): Perez; Osario, Moreno, Rodriguez, Salcido; Juarez (Hernandez 55), Torrado, Marquez; Dos Santos,Franco (Blanco 62), Vela (Barrera 32).
Subs (not used) Ochoa, Michel, Aguilar , Magallon, Torres, Castro, Guardado, Bautista, Alberto Medina