"We moved forwards in an assault column before taking our positions close to the shop. We had made several circuits of the supermarket and got very close. We wanted to see what state the entry points were in, in order to plan our assault."
At first they wanted to take him alive. But, on observing his behaviour, they realised he wanted to die in a shoot-out with the police.
"Sincerely, one of the things that most motivated us was that video of the odious assassination of our colleague Ahmed Merabet outside Charlie," said Jean-Pierre. "We all had that image in our heads." Stan said that they were initially told there were five hostages inside, but that figure could not be confirmed.
"We had managed to make telephone contact with one of the clients who was hiding in the cold store in the basement. They told us that there was a 1-month-old baby inside that room. The baby would only have survived for two hours inside there. But we were able to cut the electricity."
Another hostage, Rudy Hada, and an unnamed woman were also hidden in the cold store with the baby's mother, Sarah Bitton.
Coulibaly had pulled down the shutters around the shop, but the police realised it was possible to see inside. Six hostages were on the ground floor.
"Our snipers could not risk taking a shot at him, because there were advertising posters all over the windows and it was impossible to get a clean shot," said Stan.
The terrorist then told the hostage negotiator, who had managed to establish telephone communications, that he wanted to be allowed to broadcast live on a TV channel - in exchange for releasing a boy of around 10 years old. The authorities decided not to allow that.
Jean-Pierre said that the end of both siege situations - in the Vincennes supermarket, and in Dammartin-en-Goele, where the Kouachi brothers were holed up - was planned to take place simultaneously, just before nightfall.
But in the end the Kouachi brothers decided to come out at around 5pm - at the same time that Coulibaly was praying - and so both operations began at the same time anyway, regardless of the plan.
Two sticks of explosives had been placed on the door of the supermarket, ready for the team to blow their way in.
"The terrorist immediately opened fire on us," said Stan. "He shot at us with his Kalashnikov. Then he retreated into the shop."
A third member of the team, "Marc", told Le Parisien that they faced a "hail of bullets" from Coulibaly.
"In front of us we had a man, ultra precise, well trained, who knew how to work his AK47," he said.
Coulibaly had placed shopping trolleys in the doorway, which impeded their entry.
"Then he threw himself at us," said Stan.
He was met with fire from the police, ending up with at least 40 bullets in his body.
"It was like a bomb had gone off in there," said Marc.