Brutal storms with winds gusting up to 224 kilometres per hour (140 miles per hour) left five people dead on the French Mediterranean island of Corsica early Thursday, including a 13-year-old girl, authorities said.

It was the third day of intense rains across much of southern France that had produced flash floods and lightning, but left no casualties until now.

The Meteo France weather service also issued another severe weather alert for the island, though it said it "expected wind gusts with storms overnight to Friday will be much less violent than those on Thursday morning".

The 13-year-old was killed when a tree fell onto her bungalow at a campground near Sagone, on the island's rugged western coast, where nine others were also injured, including one seriously, rescue workers told AFP.

At a nearby beach in Coggia, a 72-year-old woman died after the roof of a beachside hut was blown off and landed on the vehicle she was in, regional authorities said.

"I was woken around 7:30 am by a very huge storm" that knocked out both electricity and mobile phone networks, said Benjamin Roux, a 26-year-old tourist, at the beach near where the woman was killed.

He had been planning to go scuba diving, but instead helped the passengers of a boat who were sleeping aboard when it was suddenly thrown onto the shore by the waves.

"They managed to get out without injuries, but they're just devastated," he told AFP.

Further north near the resort of Calvi, a 46-year-old Frenchman was also killed at a campground, and a 23-year-old Italian woman suffered serious injuries while camping nearby.

Maritime authorities later said a fisherman had died near Girolata, and a female kayaker near Erbalunga, north of Bastia.

"Her body has just been recovered from the sea," a maritime authority spokesman said, adding that around "a dozen injured" had been reported in various boats.

"Several rescues of pleasure boats" were also undertaken near the capital Ajaccio, said Jean-Jacques Peraldi, head of the SDIS fire and rescue service.

Maritime authorities reported 60 to 70 sea rescue operations, mainly along the western coast that bore the brunt of the overnight storm, which Meteo France said was now moving towards Italy.

In Tuscany, two people died Thursday after being hit by falling trees as violent winds and rain pummelled the region, and 100 others were evacuated, authorities said.

French authorities had urged people to avoid travel and take other precautions after storm alerts were issued Wednesday for several Mediterranean departments, but also along the Normandy coast and near the southeastern city of Lyon.

Around 35,000 homes on Corsica remain without electricity, power provider EDF said.

Interior Minister Gerald Darmanin, who last week visited the sites of several wildfires that have scorched thousands of hectares across France, said he would travel to the island later Thursday.

"I offer all my support to Corsicans who have faced these violent storms," he tweeted.

Less damage was reported Thursday on the mainland, however, despite another night of heavy rainfall, with the mayor of Marseille, Benoit Payan, tweeting that "more rain fell in 24 hours than the total since the beginning of the year".

A village near Montpellier, Lauroux, saw the storm dump 123 millimetres (4.8 inches) in just a short period overnight, Meteo France said.