The alleged plot centered on the national commando training center in Port-Vendres, near Perpignan, said Agnes Thibault-Lecuivre, and was due to be carried out in late 2015 or early 2016.
The suspects planned to film the scene with a GoPro camera, she said.
Interior Minister Bernard Cazeneuve said Wednesday that the suspects, ages 16 to 23, were arrested in four parts of France at dawn Monday on suspicion of planning a terrorist attack against "military installations."
One of them is a former sailor in the French navy, he said in a statement.
Thibault-Lecuivre said the youngest of the suspects had been released from custody as of Thursday.
Investigators identified the "main instigator" in the alleged plot through his "activism on social networks and relations with French jihadists currently in prison," according to Cazeneuve.
The main suspect, whom authorities had previously questioned, had a desire to travel to Syria, the minister said.
An investigation opened last month by the Paris prosecutor's office, which handles counterterrorism cases throughout France, enabled authorities to identify other individuals connected to that suspect, Cazeneuve said.
The investigation into the alleged plot is ongoing.
No link to blasts at petrochemical plant
No link has been made at this point between the people detained and explosions this week at a petrochemical plant in southern France, Cazeneuve said.
Authorities are still investigating the simultaneous blasts early Tuesday that hit two tanks containing chemicals, setting off huge fires at the plant in Berre-l'Etang, northwest of Marseille, according to CNN affiliate BFMTV.
Environment Minister Ségolène Royal told BFMTV on Thursday that terrorism wasn't the main lead in the investigation into the fires.
Since the deadly terrorist attacks in Paris in January
, which targeted the offices of satirical Charlie Hebdo magazine and a kosher supermarket in Paris, French officials have repeatedly warned of a continuing threat.
"Every week, we stop, we prevent, we avert terrorist acts," President François Hollande said this week during ceremonies to mark Bastille Day.
Cazeneuve said Wednesday that 1,850 French citizens or people who usually reside in France are implicated in jihadist networks, including close to 500 currently in Syria or Iraq.
Last month, the nation was shocked by an attack in which a man on France's terror watch list allegedly decapitated his boss before launching an attempted suicide attack
at a U.S.-owned chemical factory near Lyon.