The helicopters were reported to be heading to a gorge in northwestern Argentina for the filming of the reality TV show "Dropped" for the French broadcaster TF1.
Eight French passengers and the choppers' two Argentinian pilots died in the midair crash near the town of Villa Castelli in La Rioja province, Argentina's state news agency Telam reported, citing local authorities.
The dead included the famed sailor Florence Arthaud, who in 1990 broke the record for crossing the North Atlantic alone; the swimmer Camille Muffat, who won three medals at the 2012 Olympics in London; and the boxer Alexis Vastine, who won a bronze medal at the 2008 Olympics in Beijing.
Members of the TV production team were among the other French victims, French authorities said.
'I'm shaking, I'm horrified'
Former French soccer star Sylvain Wiltord, a contestant on the show who wasn't involved in the crash, expressed his shock.
"I'm sad for my friends," he tweeted. "I'm shaking, I'm horrified, I'm lost for words."
Muffat's boyfriend, William Forgues, told CNN's French affiliate BFMTV of his shock at hearing the news of the 25-year-old swimmer's death.
Clearly emotional, he said her agent had called him soon after midnight, herself in tears, to tell him of the crash.
Muffat, he said, was known as "madame 100%" because she succeeded in so many things.
He said she was happy and satisfied to be taking part in the show. "To be over there was her choice, 100%," he said.
At the 2012 London Olympics, Muffat won the gold medal in the 400-meter freestyle, silver in the 200-meter freestyle and bronze in the 4×200-meter freestyle relay.
Stars 'made France shine so brightly'
French President Francois Hollande expressed his condolences to the families of the victims in a statement.
The sports stars "made France shine so brightly" during their careers, the statement said.
The crash happened within moments of takeoff in good weather conditions, Telam reported, citing witnesses who spoke to a local radio station.
The helicopters, which belonged to local governments in the region, collided about 100 meters (328 feet) above the ground, the news agency said.
Police and investigators were at the scene of the crash.
A manslaughter investigation has been opened in France into the incident, to be led by the Air Transport Gendarmerie, a representative for the Paris prosecutor's office said Tuesday. It is standard procedure to launch an investigation if French nationals die abroad.
Five national police officers were en route from Paris to Argentina on Thursday, authorities said. Their mission there is to collaborate with the Argentinians and assist in the identification of victims.
The TV show involved sports stars being helicoptered into remote areas while blindfolded and then having to survive in the wilderness, according to French media.
"We learn with immense sadness of the accident that occurred during the filming of the show 'Dropped,' " TF1 said in a brief statement.
TF1's staff "come together in this terrible time with the pain of the families and those close to the victims," it said.