David Nalbandian and Horacio Zeballos beat Julien Benneteau and Michael Llodra 3-6 7-6 7-5 6-3 after a remarkable comeback from 4-1 down in the third set.
Zeballos, who had a poor opening set, lifted his game to complement experienced Davis Cup campaigner Nalbandian, a former world number one, and stun the French pair who won only three of the last 14 games in windy conditions.
World number eight Jo-Wilfried Tsonga, who won the opening point for France when he beat Carlos Berlocq in five sets on Friday, is scheduled to meet Juan Monaco in Sunday's first singles and will be trying to save the tie for France.
French captain Arnaud Clement was still hopeful.
"The two matches tomorrow will be just as hard to win for the Argentines," he said.
"I'm still confident, we still have our chances to pass this round. If we want to win the Cup we have to be able to turn this situation around."
Gilles Simon, who lost Friday's second singles to Monaco, is due to face Berlocq in the fifth rubber.
But Simon, chosen in preference to Richard Gasquet who has ankle trouble, complained of back pain during the second set on Friday and could be a doubt for Sunday.