"The sudden death of our fellow French nationals is a cause of immense sadness," a statement from French President Francois Hollande's office in Paris said.
It added that several members of the ALP TV production company involved in shooting the adventure show "Dropped" for private TV station TF1 were among the dead.
TF1 issued a statement expressing sadness and solidarity for the families of the victims. "Dropped" involves contestants being left in the wilderness and having to use their skills to find their way back to civilisation.
Arthaud, 57, was one of the first women to carve a place for herself in the world of sailing and in 1990 secured the record for the fastest solitary crossing of the North Atlantic, according to her publisher's site.
Muffat, 25, won 400 metres freestyle gold at the 2012 London Olympics. Vastine, 28, won bronze at the Beijing 2008 Olympics.
"I am sad for my friends, I'm shaking, I'm horrified, I can't find the words," Tweeted Sylvain Wiltord, ex-footballer for English Premier League club Arsenal and fellow cast member.
The victims included the helicopters' two pilots, Cesar Angulo, La Rioja's security chief, told reporters earlier.
"There were no survivors, according to the information we have," Angulo said.
Argentina's official news agency Telam said one of the helicopters belonged to the provincial government and the other to organizers of a survival competition that had been held for three years near the village of Villa Castelli.