The helicopter, an Airbus EC135 operated by a private firm, crashed Tuesday evening around the town of Bonvillard just outside Albertville, one of the main resorts in the French Alps.
The Préfet for the Savoie département, Pascal Bolot, said of the five passengers and pilot on board only the pilot had survived but was badly injured.
Despite difficult weather conditions with fog at the crash site 1,800 metres above sea level, he was evacuated to hospital.
Bolot said it was the pilot himself who had raised the alarm.
He added that an investigation has been opened by the prosecutor for Albertville but did not offer any explanation over how the crash happened.
French Interior Minister Gérald Darmanin is also due at the scene later on Wednesday. Investigators from France's Bureau of Enquiry and Analysis (BEA) agency for aviation are also set to arrive.
Le capitaine Amaury L. et le brigadier Stéphane L. de la CRS Alpes ont trouvé la mort en Savoie dans un accident d'hélicoptère lors d'une mission d'entraînement au secours en montagne.
Nous pensons aux familles.
Tout notre soutien aux montagnards des CRS. pic.twitter.com/UxYDg5xX6E
— Police nationale (@PoliceNationale) December 8, 2020
Two of those killed were members of the police unit responsible for mountain rescues – a captain aged 45 and a brigadier aged 39 – who were taking part in a training exercise, France's national police force said on its Twitter account.
The other three killed were employees of the private firm that operated the helicopter and also employed the pilot.
Pour sauver des vies, ils prennent tous les risques. Ce soir en Savoie, 3 membres du Secours aérien français et 2 CRS Alpes ont succombé à un crash d’hélicoptère. Une personne, blessée, se bat pour vivre. Soutien de la Nation aux familles, amis et collègues de ces héros français.
— Emmanuel Macron (@EmmanuelMacron) December 8, 2020
“To save lives, they take all the risks,” President Emmanuel Macron said in a tweet, paying tribute to those killed and the pilot “fighting for his life”.