Gallas had been a doubtful starter for the June 11-July 11 finals in South Africa because a calf muscle injury but took part in France's first two warm-up games, against Costa Rica last week and Tunisia on Sunday.
The defender pulled out of jogging on a beach at France's base on the French Indian Ocean island of Reunion, the spokesman said.
Gallas later turned up at a training session at Saint-Pierre, the island's second largest city, where France will play China in their last game before the finals on Friday.
After jogging around the pitch a few times, however, he left and did not take part in the session, watched by some 3,000 noisy fans and during which Sebastien Squillaci paired with Eric Abidal in central defence.
"He (Gallas) started feeling unwell during the night, with a sore stomach, and started running but had to stop," the spokesman said. "This has nothing to do with his calf."
The back four has been a concern for France lately, the team looking shaky in defence and conceding an early goal in a 2-1 win over Costa Rica last week, then again in a 1-1 draw with Tunisia on Sunday.
So concerned about Gallas was coach Raymond Domenech that he picked four centre backs in his 23-man squad for the World Cup, where France will face hosts South Africa, Mexico and Uruguay in Group A.
