Monaco's victory was vital if Argentina were to have any real chance in the tie after Jo-Wilfried Tsonga had prevailed over Charly Berlocq in five sets to put France ahead.
Monaco had been on a poor run of form but he overcame this, as well as the pressure of expectation, to record a 7-6 (7/2) 6-2 6-4 victory over Simon, who had only been drafted on to the team on Friday following Richard Gasquet's withdrawal.
Tsonga had earlier beaten Berlocq 4-6 6-2 6-3 5-7 6-2 in a draining match lasting just seven minutes short of four hours.
The 30-year-old Argentinian broke Tsonga in the opening game and went on to take the first set with Tsonga having to wait until the fourth game of the second set for his first break.
The Frenchman took some time to get into his stride with his opponent proficient from both the baseline as well as at the net.
However, once he found his groove, Tsonga took control, reeling off the second and third sets.
Berlocq though belied the 63-place gap in the rankings, although he enjoyed some good fortune in the 11th game of the fourth set when the umpire ruled there had been a double bounce when Tsonga retrieved a drop shot at the net.
The Argentinian broke Tsonga again but the Frenchman underlined his quality as he romped through the fourth set, winning on his fourth match point.
Defending champions Czech Republic coped with the absences of Tomas Berdych and Radek Stepanek to take a commanding 2-0 lead over Kazakhstan on day one of their World Group quarter-final.
With Berdych missing the tie with a shoulder injury and Stepanek rested on day one on his return from neck surgery, Czech Republic relied on Lukas Rosol and Jan Hajek to give them a 2-0 lead.
Hajek put the Czech Republic ahead in the opening rubber as he defeated Mikhail Kukushkin, a player ranked 62 places below him at 156, with a 6-3 6-2 6-4 victory in under two hours on the clay courts of the National Tennis Centre in Astana.
Rosol had to work harder for his victory, overcoming Andrey Golubev in four demanding sets in what was the world number 63's first Davis Cup victory in a live rubber.
Golubev managed to save one match point in the tie-break in the fourth set before Rosol claimed a 4-6 6-4 6-2 7-6 (8/6) win to give his country a 2-0 lead, adding extra importance to Saturday's doubles when Czech Republic could secure the tie.