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The French Rugby Federation (FFR) also said head coach Fabien Galthie has tested positive for the virus.
It was another figure from within the France camp, who was not named, that returned a positive result following testing on Monday.
Announcing that news, the FFR said: "Following the PCR tests carried out last night in Marcoussis with the France XV, all the players tested negative, a member of the technical staff tested positive, as well as a suspicious and unproven case concerning Fabien Galthie who will be tested again this morning.
"In accordance with health protocol, all members of the team and management were isolated this morning. Interactions are kept to a minimum.
"An additional test at the National Rugby Centre will be carried out on Wednesday morning for the entire squad."
The squad are due to disperse later this week to be allowed a short time at home between matches, with France, who have won their opening two games, not in action again until they face Scotland on February 28 in Paris.
France scored a fine 15-13 win over Ireland in Dublin on Monday (AEDT) to follow up the opening 50-10 victory over Italy.
The FFR statement said: "Tests will be carried out at home on Friday, as well as on Sunday evening at the National Rugby Centre when the squad reunites.
"The announcement of the 31 players for the Scotland match will take place this Wednesday evening, February 17."