But after opening up a two-set lead they wasted two match points in the third set before they settled the affair with a commanding final set performance.
"We have the potential to beat (America's top players) Andy Roddick and James Blake," said French captain Guy Forget.
"I'm not worried about it but we will have to play three perfect matches."
In Moscow, Australian Open champion Novak Djokovic and Nenad Zimonjic kept alive Serbia's chances by defeating Russia's Mikhail Youzhny and Dmitry Tursunov 6-3, 7-6 (8/6), 7-6 (7/5).
That made the overall score 2-1 ahead of Sunday's reverse singles.
"I'm happy that we're still in," said Djokovic who missed the singles on Friday because of flu.
"It was not really encouraging as we were 2-0 down after the first day with our three best players injured or sick but today we played solid tennis."
The winners of the tie will face the Czech Republic, who defeated Belgium 3-0, in the last eight.
Tomas Berdych and Radek Stepanek beat Olivier Rochus and Kristof Vliegen 6-7 (2/7), 7-6 (8/6), 7-5, 5-7, 6-4 in the doubles in Ostrava as the Czechs made the quarter-finals for the first time in six years.
"It's a relief to go through," said Stepanek.
Argentina eased into the last eight when David Nalbandian and Jose Acasuso beat Jamie Murray and Ross Hutchins 6-2, 7-6 (13/11), 6-0 in the doubles for a 3-0 win over Great Britain in Buenos Aires.
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