The 30-year-old lost control of his skis and slammed into the snow before sliding into protective netting on Friday while training for the World Cup downhill race being held this weekend in Bormio, Italy.
Sarrazin was airlifted to hospital and the FFS initially said he was "conscious" before later revealing that he sustained internal bleeding in his head from the impact.
"Cyprien Sarrazin was operated on overnight to reduce pressure from the intercranial haematoma," the federation said in a statement.
"The surgery went well. For now he remains under anaesthesia," it said, adding that more information would be released later Saturday.
Sarrazin enjoyed his best campaign on the World Cup circuit last season, with four victories including a downhill win at Bormio, but is yet to win in 2024/25.
He clocked the best time during his first training run on Friday and was leading at the halfway mark during his second on the Stelvio piste -- which will host alpine skiing events at the 2026 Winter Olympics -- before losing control.
Two other skiers had serious accidents during their second training runs on Friday, sparking questions about the preparation of the Stelvio, one of the most difficult on the circuit.
Italy's Pietro Zazzi was also taken to hospital by helicopter after suffering a double leg fracture. He was due to undergo surgery in Milan on Saturday.
'Don't deserve Olympic Games'
Although Bormio is a staple of the World Cup calendar and has twice hosted the world championships -- in 1985 and 2005 -- it regularly comes in for criticism from skiers.
"They don't know how to prepare a course. They've been preparing courses for 40 years and they don't know how to do anything other than prepare dangerous slopes," Frenchman Nils Allegre told Eurosport.
"They don't deserve to have the Olympic Games here."
Race director Markus Waldner of the International Ski and Snowboard Federation (FIS) defended the course preparations and said conditions ahead of training had affected the snow.
"Now there's criticism every week: in Gurgl (Austria) the track was too hard, in Levi (Finland) too smooth... We are an outdoor sport," Waldner said after a meeting of team captains Friday in Bormio.
"The organisers do their best to prepare the slopes as well as possible and (the Stelvio) was prepared as it is every year," he said.
"The problem is that on Christmas Day there was a lot of wind, and we know what wind does. It dried the snow from the bottom towards the top, which explains why the snow was not uniform on the three-kilometre run, which is impossible to make uniform."
Waldner, who has held his position in charge of the men's World Cup since 2014, said he believed the main problem is the evolution of equipment that allows skiers to go increasingly faster.
"It's too aggressive, we've reached the limits, there's no margin left. It's difficult to find the right skis that work on the hard sections and then on the softer sections. That's the problem, if you go to the limit, you get what happened on Friday," he said.
"We need everyone's cooperation. The equipment manufacturers listen to us, not the biggest national federations," he added.
