The suspect, who has been named as 25-year-old Moroccan national Ayoub El Khazzani, was wrestled to the floor by three American passengers after opening fire with an assault rifle on Friday evening, and is now being interrogated by counter-terrorist officials near Paris.
A Spanish counter-terrorism source said he had lived in Spain for seven years until last year and had travelled to Syria from France.
French Interior Minister Bernard Cazeneuve confirmed that Spanish intelligence services had flagged the man to France "due to his membership of the radical Islamist movement."
A 28-year-old French passenger spotted the gunman as he exited a toilet cubicle and tried to disarm him, but Khazzani slipped away and fired several shots.
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Then a Franco-American traveller in his 50s clashed with the man and was shot and wounded. But the attack was quickly stopped when two off-duty US servicemen and their friend charged the gunman and restrained him.
"I looked back and saw a guy enter with a Kalashnikov. My friends and I got down and then I said 'Let's get him'," Alek Skarlatos, a 22-year-old member of the National Guard in Oregon who recently returned from Afghanistan, told France's BFMTV.
"At that point I showed up and grabbed the gun from him and basically started beating him in the head until he fell unconscious," said Skarlatos.
His friend Anthony Sadler, a 23-year-old student at Sacramento State University, and a British business consultant, Chris Norman, then helped keep the man subdued.
Norman, 62, said he thought the suspect's gun may have jammed, preventing more bloodshed.
"My first reaction was to hide but... My thought was I'm probably going to die anyway, I'd rather die being active, trying to get him down than simply sit in the corner and be shot," he told reporters.
With the man floored, Skarlatos left to search for more gunmen, while Norman helped tie up the attacker with his tie.
Despite his own injuries, Stone then went to help the man who had been shot in the shoulder. Both were hospitalised but are said to be recovering well, and Stone was released later Saturday after surgery on his hand.