The Serbs took an unlikely 1-0 lead on Friday as world number 80 Dusan Lajovic, acting as his nation's top player with both Novak Djokovic and Viktor Troicki absent, beat Lucas Pouille in four sets in Lille.
He won 6-1 3-6 7-6 7-6 at Stade Pierre-Mauroy before Jo-Wilfried Tsonga levelled affairs by beating Laslo Djere in straight sets.
The big-serving star won 7-6 6-3 6-3 and it is the French who will take an advantage into Sunday's reverse singles after Pierre-Hugues Herbert and Nicolas Mahut beat Filip Krajinovic and Nenad Zimonjic 6-1 6-2 7-6 in the doubles.
The French pair, who have won two Grand Slams together, dominated on serve in the first set and although their opponents improved, it was a one-sided contest.
Tsonga is set to face Lajovic on Sunday and victory will see France into the final for just the second time in 15 years.