France were already missing five of the side that started in the win over Ireland eight days ago, including the talismanic scrum-half Antoine Dupont. Coaches Fabien Galthie and William Servat have also tested positive.
Now captain Charles Ollivon is among five more players – four of whom were involved against Ireland – to test positive.
France have continued to call up new players, and are due to reassemble for training on Wednesday.
On Thursday, the French Health Minister said all those who tested positive would need to stay away from the group for 10 days.
France, who have won their opening two matches of the campaign, will continue to test their players every day in the hope of fulfilling the fixture against Scotland in Paris.
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