Gusts of up to 130 kilometres (80 miles) per hour lashed the region, prompting the state weather service Meteo France to issue its second-highest alert and warning against people using their cars.
The state electricity company EDF said power was cut to 385,000 homes, 200,000 of them in Normandy northwest of Paris and in the northeastern Pas-de-Calais region, and emergency services said they had received thousands of calls because of falling tiles, branches and downed power lines.
Three of those who died were victims of falling trees. A 61-year-old woman died in a chic western Paris neighbourhood when a tree came crashing down on her car, police said, while a motorcyclist was also hit in the capital.
A cyclist in the Somme region of northeastern France was also crushed by an uprooted tree.
Meanwhile an unidentified man aged 28 believed to belong to a Gypsy community was killed when he fell off a roof he was repairing in the western suburb of Vernouillet after a piece of metal sheeting he was standing on was dislodged.
Earlier police reports said that the man had been decapitated by the piece of metal.
Parks, cemeteries, gardens and the Eiffel Tower in Paris were closed.
The famous Chateau of Versailles near the capital was also shut and visitors were evacuated. The property is still recovering from a 1999 Christmas storm which uprooted more than 10,000 trees on its grounds -- a storm which caused major damage notably to forests across much of northern and eastern France.
The main Paris airports of Charles de Gaulle and Orly were also hit, prompting delays of an hour for around 50 flights and some cancellations. Airport authorities warned travellers of delays lasting into the evening.
Many trains in northern France were brought to a standstill, with delays hitting commuters on their way home for the weekend.
In Normandy, a high motorway bridge spanning the Seine river was buffeted by winds that knocked over a truck and a caravan, without causing injuries. Officials closed the structure after the incidents.
Falling trees also injured the occupants of cars in two communities southwest of Paris and in northern France.