The first drone sighting was near the US embassy in the French capital. The Eiffel Tower, the Place de la Concorde and the Invalides military museum "were also flown over" in the early hours of Tuesday, the source said.
"It could be a coordinated action but we don't know for now," the source, who asked not to be identified, said. "We did everything to try and catch the operators but they were not found," another source close to the investigation said.
However until today "there have never been so many drones appearing in one night," the security source said.
French law bans small, civilian drones from areas such as nuclear facilities, which are protected by a no-fly zone that spans a 1.6-mile radius and a height of 1,000 metres.
Despite a heightened security alert over the risk of Islamist attacks in France, police so far have been unable to identify who is behind the drone activity. Experts say that the small unmanned craft would not pose a threat if crashed into a hardened nuclear facility.