Les Bleus fell 1-0 behind after a nervous Lucas Pouille slumped to a 6-1 3-6 7-6(7) 7-6(5) defeat by Dusan Lajovic.
French number one Tsonga got off to a slow start as world number 95 Djere held throughout the opening set, but the 2008 Australian Open runner-up served three aces to take the tiebreak easily.
He was then rarely troubled in a one-sided encounter on the indoor claycourt in the Pierre Mauroy stadium.
Pierre-Hugues Herbert and Nicolas Mahut are expected to give the hosts a 2-1 lead in Saturday's doubles against Filip Krajinovic and Nenad Zimonjic.
It did not go as planned, however, for Pouille.
The world number 22 was way too shaky in Lille and rapidly fell behind against world number 80 Lajovic, bowing out after saving five match points.
"This is what Davis Cup is about," said Serbia captain Zimonjic. "Both players gave everything - they fought until the end.
"We know we need a miracle to win this tie but we believe in our team."
France were heavily favoured with Serbian former world number one Novak Djokovic absent. But Pouille looked nervous early on, spraying the court with unforced errors while Lajovic made the difference with his forehand.
Pouille fought back to force a tiebreak. But despite the loud backing of the crowd, the Frenchman wasted a set point before handing the set to Lajovic when he fired a forehand wide.
The Frenchman turned the situation around in the second set as Lajovic started to struggle with his forehand. But in the fourth set, the Serb broke early on and set up a match point at 5-3.
Pouille saved it and broke back for 5-4. He then saved three consecutive match points on serve in the 12th game, but lost the tiebreak after a brief interruption as Lajovic was suffering from cramps.
(Reporting by Julien Pretot; Editing by Larry King and Christian Radnedge)
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