Le Cleac'h, who won the single-handed Vendee Globe round-the-world race in 2017, managed to trigger his distress beacon after one his catamaran's floats snapped off in gusts of more than 35 knots and five-metre waves, race organisers said.
The Frenchman's shore team reported that he is safe inside his damaged boat, they added in a statement on Tuesday.
"It is too far away for a helicopter to go to the site, but we know ... that a plane is flying over to check out the situation. Armel is OK and is getting ready to be evacuated," Race Director Jacques Caraes said.
Tokyo 2020 - Giles Scott calls time on Olympic sailing career following second gold medal
The storm has taken its toll on the skippers in the Route du Rhum-Destination Guadeloupe, with half the six starters in the ULTIME class now out of the race, which began off the Brittany port of Saint Malo on Sunday.
While most of the 123 boats are continuing the 3,542-mile course towards Point-à-Pitre in Guadeloupe, nearly 50 are either seeking shelter along the French and Spanish coasts or heading back towards France with technical issues.
Tokyo 2020 - Eilidh McIntyre on sharing Olympic gold with 'inspirational' and 'humble' Hannah Mills
Tokyo 2020 - Hannah Mills on her second Olympic gold medal