Tokyo won the right to host the 2020 summer Olympic Games after overcoming concerns about leaking radioactive water at the stricken Fukushima plant north of Tokyo, with Japanese Prime Minister Shinzo Abe assuring the International Olympic Committee that the situation was "under control".
The cartoon, carried in the satirical Le Canard Enchaine, shows two sumo wrestlers, each with an extra leg or arm, facing off with the Fukushima plant in the background as an announcer says, "Thanks to Fukushima, sumo is now an Olympic sport."
Another cartoon shows people in protective gear by the side of a pool, the Tokyo Shimbun daily reported.
"This cartoon hurts the feelings of those who suffered through the Great East Japan Earthquake," said Chief Cabinet Secretary Yoshihide Suga, referring to the March 2011 earthquake and tsunami that wrecked the Fukushima nuclear plant, triggering the world's worst nuclear disaster since Chernobyl.
"It is inappropriate and gives a wrong impression of the Fukushima contaminated water issue. It is extremely regrettable."
Suga said Japan would lodge the complaint through the French embassy in Tokyo and that the Foreign Ministry had been directed to "thoroughly explain the situation" to avoid similar incidents.
Japan was angered last year after a French broadcaster used a composite picture that showed Japanese national football team goalie Eiji Kawashima with four arms and the caption "Fukushima Effect" about a save he made in a game between the two nations.
The broadcaster subsequently apologised.
Japan was chosen as host for the 2020 Olympics, beating out Madrid and Istanbul despite the issues posed by the Fukushima plant, some 230 km from Tokyo.
The crisis shows no signs of ending. The operator of the plant said on Wednesday that levels of tritium - considered one of the least harmful radioactive elements - spiked more than 15 times in groundwater near a leaked tank over three days this week.