The Government of National Accord, which has failed to establish control over the whole country in its battle with rival militias, protested against the "violation" on its Facebook page.
It would welcome help in fighting the Islamic State armed group by "friendly nations"; it said, but that "should be based on a request or in coordination".
Demonstrations in several towns
Hundreds of people demonstrated in several Libyan cities, most notably Tripoli and Misrata.
In Benghazi they responded to a call by the former mufti of Tripoli, Sadiq al-Ghariani, the spiritual leader of the Benghazi Defence Brigades, who claimed to have shot down the helicopter the three dead soldiers were travelling in.
France working with Haftar
Sources close to General Khalifa Haftar, who is fighting the Islamists but has refused to recognise the unity government, said the Frenchmen were military advisors.
France has been working with Haftar for several months so as to gather intelligence in the fight against IS but without taking part in combat, military sources told Le Monde newspaper.
US and British special forces are also present in Benghazi, according to the Washington Post.