Officers stopped the vehicle on Sunday at a toll station near Chambéry in the French Alps.
The car belonged to 91-year-old Argentinian cardinal Jorge Mejia, but his private secretary had handed it over to two Italian men for a service.
RTL Radio reported that the Italians believed they could bring the drugs into Italy without being stopped because of the diplomatic plates, but this has not been confirmed.
French police say neither of the men had Vatican diplomatic passports, so the Holy See is not involved in the case.
A Vatican official confirmed that the car was involved in an incident but added that none of its staff members were involved.