The shocking incident took place at La Motte-Picquet-Grenelle station in the capital's 15th arrondissement on Wednesday evening.
According to reports in Le Parisien newspaper a 24 year-old man tried to leave the carriage just as the train was about to depart in the direction of the station Charles de Gaule Etoile.
As he left the carriage the doors closed behind him but part of his jacket became stuck in the doors and he was unable to free himself, the newspaper reports.
As the train left he was dragged with it along the length of the platform.
The driver of the train only noticed at the next station, which was Dupleix, when the power was cut.
Paramedics were called, but he was pronounced dead at the scene.
Metro trains in Paris are normally unable to depart a station if the doors are not properly closed. However sometimes jackets or straps of bags can be caught in the doors without a problem being signaled to the driver.
If the reports of the accident are confirmed questions will no doubt be asked whether the system was working properly and whether it could be improved.
A spokesperson for Paris transport chiefs RATP, which is in charge of the Metro, confirmed to The Local that "a serious accident" involving a passenger had taken place at La Motte-Piquet Grenelle.
"The circumstances of the accident will be determined by the police who are currently in the process of investigating it," read the statement from RATP.
A spokesperson for Paris police also confirmed the death of the passenger but declined to comment on the details of the accident.