In the grainy footage, the attacker – a man called Ziyed Ben Belgacem who was later shot dead by security forces – can be seen approaching one of the soldiers on duty at the airport.
He appears to be following her from behind, before dropping a bag and then rushing up and grabbing on to the woman, apparently by her neck.
He then drags her towards a wall, still holding her by the neck. It's presumably at this point that the man tried to get the soldier's weapon.
In the footage, embedded below or featured on BFM TV here, the crowd doesn't seem to notice that the man has taken the woman hostage.
The attacker is also understood to have put a gun to the soldier's temple and seized her weapon, although this can't be clearly seen in the video.
He then walks with the woman away from the camera, as two other soldiers approach from behind. After about one minute since the woman was taken, one of the other soldiers can be seen taking aim with his own weapon.
Seconds later, the attacker is lying on the ground – presumably dead already – and the woman moves away from him.
Investigators are still trying to understand what motivated Saturday's assault by the 39-year-old man, which led to a major security scare and the temporary closure of the capital's second-busiest airport.
Toxicology tests carried out on Sunday showed he had an alcohol level of 0.93 grams per litre in his blood, and the presence of cannabis and cocaine.
The attacker had also fired at police in a northern Paris suburb earlier that morning.
The attack at Orly comes with France still on high alert following a wave of jihadist attacks that have claimed more than 230 lives in two years.
The violence has made security a key issue in France's two-round presidential election on April 23 and May 7.