The 35-year-old speed specialist, who competed for France at the 2010 and 2014 Winter Olympics, was training in the resort of Nakiska in Canada.
"According to the information currently available to the French Ski Federation, David Poisson reportedly dropped heavily after losing a ski during the shared training session with other nations that took place in Nakiska," the statement read.
The Federation added that they had been in contact with Poisson's family "to support and accompany them in this terrible event."
Fabien Saguez, the national technical director, and David Chastan, director of the French men's Alpine Ski team, were traveling to Canada, said the FFS, to support family, teammates and coaching staff.
Poisson was training for the next races on the men's World Cup circuit, which are set to take place in Lake Louise, Canada, on November 25-26.
'Smile will be missed'
Lindsey Vonn, America's most decorated skier, led tributes as the greats of Alpine skiing posted their condolences on social medial.
"This is devastating," tweeted Vonn, America's most decorated skier. "My deepest condolences to his family. Rest in peace David."
America's two-time Olympic champion Ted Ligety wrote on Twitter: "Deeply shocked and saddened about David Poisson. Feeling for his friends and family."
The U.S. Ski Team also tweeted: "So sad to hear that David Poisson passed away after a training crash today in Canada.
"Thoughts and love to his family, friends and @FedFranceSki teammates."
Swiss ski star Lara Gut said Poisson's "smile will be missed."
Poisson, who came from Annecy, finished seventh in the downhill at Vancouver 2010 before coming 16th at Sochi 2014.
He also won bronze in the downhill at the 2013 World Championships in Schladming, Austria.
His French teammate Thomas Mermillod-Blondin, also from Annecy, wrote on Instagram: "Tonight I think of you, David! Our friend, our friend, our colleague, our model, the smile of the group, the quiet strength... I think of your closest family. So sad to know you're gone."
French biathlete Simon Fourcade wrote
: "So many good times spent at your side ... We will miss you."
Journalist Gernot Bauer remembered Poisson's reaction after clinching his bronze medal in Schladming four years ago.
"Will never forget the sparkle in his eyes after taking bronze in DH Schladming 2013," he posted