The woman, who was in her thirties, was carried away by strong streams of water in the street and ended up getting trapped under a car, radio France Bleu said.
BFMTV reported that the woman died on Saturday evening while being stuck under the car in Rouen. Her death was confirmed by the city authorities.
Around 5,000 people were left without electricity in France on Saturday night amid a major thunderstorm, French power grid operator Enedis said. An orange alert level was issued for a total of 65 departments.
BFMTV reported that the Eiffel Tower was struck by lightning on Saturday night. French photographer Bertrand Kulik managed to capture the moment and posted his photos on social media.
ZZ/PR