Benjamin Kayser and Aurelien Rougerie suffered arm injuries while Julien Pierre was hurt on the hip after being assaulted in the early hours of Sunday morning, according to their club Clermont Auvergne.
All three were left with "deep cuts", although their injuries are not life threatening, Clermont said.
The trio, who were walking back to their hotel when the attack occurred, had been on a night out in the Millau area of southern France.
A statement posted by the club on their official website on Sunday read: "While returning on foot to their hotel in the night from Saturday to Sunday, a group of Clermont players was attacked by a dozen individuals armed with machetes, knives, swords.
"The whole club is both shocked and outraged by these facts and [will] provide all the necessary support to local authorities [who] have opened an investigation into the attack to find and punish the perpetrators.
"In addition to complaints by individual players involved, the club also contemplates judicial proceedings.
"We will as soon as possible [provide] more information on the health of our players."
Clermont captain Rougerie, 33, is the most experienced of the trio having been capped more than 70 times at international level.
