Hail, heavy rain and winds peaking at 224 km per hour (140 mph) swept the island early in the day. Two of the victims were killed when trees fell in campsites.
"Storms formed at sea will affect large parts of the western Corsica coast throughout the night from Thursday to Friday," Meteo France forecaster said.
French President Emmanuel Macron said he had called an emergency government meeting by video conference on Thursday evening to respond to the crisis.
Visiting Corsica, Interior Minister Gerald Darmanin said that at one point about 350 people had been reported missing as pleasure boats had capsized or been thrown adrift, but he added they had now all been found alive and well.
Witnesses of the morning storm, which wrecked campsites, delayed trains and uprooted trees, said they had never seen anything like it on the island.
"We have never seen such huge storms as this, you would think it was a tropical storm," said Cedric Boell, manager of the restaurant Les Gones Corses in northern Corsica, who saw two pleasure boats tossed on to nearby rocks.
Yolhan Niveau, 24, a wildlife photographer staying at a campsite near San-Nicolao in the northeast of the island, said the storm had torn through the site, uprooting trees and damaging mobile homes.
"There was no warning. ... I don't feel scared just stupefaction. No one expected this," Niveau said.
In central Italy, two people were killed by falling trees on Thursday as powerful storms battered several regions.
'TORNADO-LIKE GUSTS'
The storm raged as many areas of France - which has been hit by heatwaves and severe drought - saw more rain in a few hours than in recent months combined.
In southern Corsica, a 13-year-old girl died when a tree fell at a campsite and a 72-year-old woman was killed when her car was struck by a beach hut roof, authorities said.
A 46-year old Frenchman died when a tree fell on a campsite bungalow in the north, authorities said. A 23-year-old Italian woman was injured at the same location and taken to hospital in critical condition.
A fisherman and someone who was out canoeing also died, authorities said. Interior Minister Darmanin did not give details on the sixth death.
Meteo France, which said that the exact location of storms was hard to predict, had not given advance warning. It issued an alert with "immediate effect" as strong winds began to hit the island.
On France's mainland, households were left without power after a storm hit the southern Loire and Ain departments, while on Wednesday evening in Marseille, streets were flooded and streams of water ran down steps in the port city, videos shared on social media showed.
Further north, drought has left the river Loire, famous for the chateaux along its banks, so shallow that even flat-bottomed tourist barges could barely navigate it.
(Reporting by Tassilo Hummel, Myriam Rivet, Matthieu Prottard, Layli Foroudi, Marc Angrand and Geert De Clercq; Writing by Ingrid Melander; Editing by John Stonestreet, Nick Macfie and Jonathan Oatis)
By Marc Angrand and Benoit Van Overstraeten
