The sister-in-law of Prince William was snapped in Paris driving around in a convertible with French fashion entrepreneur Arthur de Soultrait while a friend brandished a handgun.
France is experiencing a heightened security alert after Islamic terrorist Mohammed Merah used a handgun to murder seven people in the south west of the country in MArch.
And on the weekend, two men were also arrested in the Paris area at the weekend in connection with four murders in five months carried out with a pistol in the nearby Essonne department.
If the gun was genuine, all those involved in the incident face up to seven years in prison.
Even if the weapon was only a replica, they could be sentenced to two years.
At least one person who witnessed the waiving of the gun has made a formal complaint to Paris police, and handed over pictures of the incident.
Judicial police are now likely to involve an examining magistrate.
If they consider that there is enough evidence for a prosecution, then Middleton and Soultrait will be summoned to give evidence.