With his left arm in a sling to protect his injured hand and a cut over his right eye, Stone, 23, along with his American friends, student Anthony Sadler, also 23, and National Guardsman Alek Skarlatos, 22, gave details of what officials said was a foiled terrorist attack.
"I went over, saw that he was squirting blood out of the left or right side of his neck," Stone said. "And I was going to use my shirt at first, but I realized that wasn't going to work, so I just stuck two of my fingers in the hole, found what I thought to be the artery, pushed down and the bleeding stopped." He held that position until paramedics arrived, he said.
The French-American man whom Stone helped, and whose life he possibly saved, remains hospitalized. U.S. Ambassador to France Jane Hartley said at the news conference that he was "doing pretty well."
Stone said the man, whose name has not been disclosed, "deserves a lot of the credit" because he was the first one to try to stop the gunman, whom authorities have identified as suspected Islamist militant Ayoub el Khazzani, 26, of Morocco.
Stone thanked the doctors who reattached his thumb, which was almost severed by the gunman, who was armed with a box cutter, a pistol and a Kalashnikov AK-47 assault rifle.
The three friends, who all grew up together near Sacramento, California, were touring Europe, partly to celebrate Skarlatos' return from a recent tour of duty in Afghanistan.
The men said they had no choice but to react when they saw the gunman cocking his assault rifle. Stone said he choked him while Skarlatos hit him on the head with one of his firearms.
Stone's and Skarlatos' military training kicked in while they provided first aid and searched the train to make sure there were no other gunmen, they said.
Their civilian friend Anthony Sadler, says they couldn't just sit back and do nothing.
"Hiding or sitting back is not going to accomplish anything. The gunman would have been successful if my friend Spencer had not gotten up, so I just want that lesson to be learned going forward: in times of terror like that to please do something, don't just stand by and watch," he said.
They said the gunman was apparently untrained in firearms and that he could have used all his firepower to devastating effect if he had known more about weapons.
Skarlatos disputed a statement the gunman made, through a lawyer, that he just wanted to rob the train because he was hungry.
"It doesn't take eight magazines to rob a train," Skarlatos said. "The guy had a lot of ammo. His intentions seemed pretty clear."