At about 9.10am the man tried to hold up a BNP bank in the avenue de la Grande Armée, which runs between the famous monument and the city limits as a continuation of the Champs Elysées avenue.
Staff were present and the police arrived, shooting once he was outside the bank.
He was wounded in the thigh and the thorax, the police said.
Emergency workers gave him medical treatment in the street and he was taken to a Paris hospital.
The suspect already has a police record for armed robbery and violent crime, police sources told the AFP news agency.
Bank raids declined 66 percent between 2013 and 2016, according to figures by the organised crime unit, OCLCO.