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Aurelien Rougerie, Julien Pierre and Benjamin Kayser were attacked by a 12-strong gang in Millau, southern France, in the early hours of Sunday morning.
A club statement said none of the players' injuries were life-threatening, adding that weapons used included machetes, knives and swords.
The players had been to a nightclub and were walking back to their hotel when they were set upon by the gang for no apparent reason, police said, adding that no-one was detained at the scene of the attack.
Pierre, who along with Rougerie was part of the France team that lost the 2011 World Cup final, will have surgery on "deep cuts" to his hip.
Clermont captain Rougerie, aged 33 and capped 77 times by his country, and Kayser have injuries to their arms from the attack in Millau, where the players were staying before heading to a club training camp.
"We are deeply shocked and outraged by these acts and will bring all the necessary support to local authorities who have launched a probe," Clermont said in a statement.
Kayser, 29, has played 24 times for France and Pierre, 32, has 27 caps.