Radio contact was lost with the aircraft as it carried out a search mission between Marseille and Saint Tropez on the storm-lashed Mediterranean coast.
An investigation has been launched into the cause of the tragedy.
It is thought poor visibility caused by fog may have been a contributory factor.
Police have sealed off the crash site in the hills north of Marseille and officers are scouring the area.
Interior Minister Christophe Castaner has described the three victims as “everyday heroes who gave their lives to protect the French”.
Authorities in the region said two other people had also died following torrential rain, including a stable owner whose vehicle was swept away by floodwater as he tried to check on his horses.
It comes after six people were killed in floods along the French Riviera a week ago.
Torrential rain has led several rivers to burst their banks in the southeastern part of the country, causing major damage to homes and causing transport disruption.