The robbers had handguns but did not fire any shot's during Sunday night's attack, the Paris prosecutor's office said.
The car was carrying about 250,000 euros (£200,000) in cash and official embassy documents, a police spokesman said. The gang seemed to be well-informed about the vehicle's itinerary, he added.
The Paris prosecutor's office would not confirm the theft of cash or documents but admitted "things of value" had been taken.
The Mercedes car, with a driver and two passengers, was heading for the city's Le Bourget airport to handle paperwork for the departing prince.
Le Bourget airport is often used for high-level visitors taking private jets to Paris.