Interior Minister Bernard Cazeneuve said security forces had staged dawn raids on Monday to take into custody four people, aged between 16 and 23, who were "planning to commit a terrorist act against French military installations."
A source close to the investigation into the thwarted attack, who asked to remain anonymous, said the four arrested had been planning to film the decapitation of a member of the military based in southern France.
One of the four people arrested had served in the navy, Cazeneuve said.
The youngest suspect was later freed, a judicial source told AFP.
The mastermind of the foiled attack had been planning to travel to jihadist-controlled areas of war-torn Syria, Cazeneuve said.
The news of the arrests followed a statement from President Francois Hollande, who said attacks had been thwarted in recent days.
"This week, we stopped terrorist attacks which could have taken place," Hollande said on a visit to the southern city of Marseille.
France remains on high alert more than six months after jihadist attacks in January that claimed 17 lives and started with shootings at satirical magazine Charlie Hebdo.
At traditional July 14 celebrations, Hollande said: "Every week, we are arresting, preventing ... Terrorist acts."
The suspected plotters are now in the custody of France's intelligence services, the DGSI, and anti-terrorist prosecutors in Paris have opened a probe, Cazeneuve said.
"I want to congratulate our security services for this new blow to the terrorists and for again foiling an attack," said the minister.
There are 1,850 French citizens or people living in France who are "implicated" in jihadist networks, with around 500 in Syria or Iraq, authorities said.
France, which is home to Europe's largest Muslim population, has beefed up security, posting 30,000 police officers and soldiers outside 500 sites deemed "sensitive" such as schools and places of worship.
Authorities have also set up a hotline for friends or family concerned that someone could be tempted to wage jihad -- an effort that has yielded 2,500 leads.
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