The man says he once requested an Uber driver from his wife's phone.
Despite logging off, the application continued to send notifications to her iPhone afterwards, revealing his travel history and arousing her suspicions.
The couple have since divorced. The lawsuit is reportedly worth up to €45m ($48m; £38m).
"My client was the victim of a bug in an application," his lawyer David-André Darmon told AFP news agency after the case was lodged at a court in Grasse.
"The bug has caused him problems in his private life," Mr Darmon added.