His body was found early on Monday, French maritime authorities said.
Another man from the same boat was rescued by friends in a nearby vessel.
In another incident, a woman motorist was crushed to death after a tree branch broke off in gale-force winds and landed on her car in southern Normandy in northwest of Paris, local media reported.
Local authorities said strong winds of up to 110kph also sank a trawler an hour off Guernsey in the Channel Islands. The crew was rescued by other fishing boats.
Another vessel, the Artemis, a Dutch-registered cargo ship, was blown onto a beach at the Atlantic coastal resort of Les Sables d'Olonne.
Thousands of homes in northwest France plunged into darkness as gales brought down power lines.
In Britain, airport authorities said dozens of flights were delayed or cancelled and train services were disrupted by falling branches on railway tracks.
Gusting winds reaching a speed of more than 130kph uprooted trees, ripped off roof tiles and damaged power lines, causing a blackout affecting 10,000 homes.
Hurricane-force winds in the Channel also forced the closure of the English port of Dover, where about 12 ferry crossings were cancelled on Monday.
British and French forecasters said further storms were expected overnight on Monday.