French No 1 Tsonga had been slotted to take on the Swiss star, but he has been struggling with an injury to his right arm following his opening day loss to Stan Wawrinka.
The French Davis Cup team announced that Gasquet would take his place.
Federer also lost on Friday in straight sets to Gael Monfils, but he was given a huge boost on Saturday when he and Wawrinka teamed up to defeat Gasquet and Julien Benneteau in straight sets in the doubles.
That gave the Swiss a 2-1 lead and needing just one more point to win the Davis Cup for the first time.
The 33-year-old Federer can now secure the decisive point against Gasquet and clinch the last big prize in tennis missing from his collection. If Gasquet wins, Wawrinka and Gael Monfils will decide the final??on the indoor claycourt at the roofed-over Lille football stadium.
With Monfils certain to take the second training slot to prepare for a potential fifth match decider against Wawrinka it was a clear indication that Tsonga would not play.
In head-to-heads Federer leads Gasquet 12-2, but both of Gasquet’s wins came on clay – in their first ever meeting in Monte Carlo in 2005 and in Rome in 2011.
Their only meeting this year resulted in a 6-1 6-2 win for Federer in the Masters Series tournament in Miami.
Sunday’s singles are due to get underway from 1200 GMT.