Clermont have released a statement on Julien Pierre, AurÃ©lien Rougerie and Benjamin Kayser, saying they should return to training in a month.
The trio, who were attacked in Millau by a dozen individuals "armed with machetes, knives and swords" on Saturday night, were all hospitalised.
Pierre was in the most serious condition but the club confirmed his operation was a success and that he will be back training before September.
Kayser suffered cuts to his arm and hand in the attack over the weekend in southern France, with his return to fitness expected to be four weeks.
Meanwhile, centre and captain Rougerie will require between three and four weeks before he is cleared for training, the club said on Monday.