"We estimate at around a dozen the number of former troops who have joined these networks," the source, who wished to remain anonymous, said.
"Our concern is not former soldiers... It's preventing the phenomenon of radicalisation with our forces," the source added.
Defence Minister Jean-Yves Le Drian refused to comment directly on the affair.
"The cases of former soldiers being tempted by jihadism are extremely rare," he told a press conference to announce new anti-terrorism measures in the wake of the recent attacks in Paris.
The army's biggest fear is that rogue soldiers could turn their weapons on their comrades or use their combat and explosives know-how to carry out attacks.
RFI radio reported that most of the
soldiers-turned-jihadists, whose ranks included former special forces and Foreign Legion members, had joined the Islamic State group.
One was commanding a group of French recruits that he had trained in northeast Syria, the radio added.
"Others are explosives experts," RFI said, adding that the fighters were mostly in their twenties.
After five years of service the soldier joined a private security firm protecting oil fields in the Arabian peninsula, the paper reported in its online edition.
"That's where he progressively became radicalised, growing a beard and subscribing to Islamist ideology," added L'Opinion, which quoted unnamed sources as saying he was fired and then travelled to Syria.
French intelligence sources said the former paratrooper was "known" to them.
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