Ziyed Ben Belgacem, 39, was killed after he put a gun to a soldier's head saying he wanted to "die for Allah".
Earlier on Saturday, he was involved in a shooting and then a carjacking.
His father told French radio Belgacem had phoned after the first attack to say he had "screwed up with a gendarme", before proceeding to Orly.
Belgacem is described as having been radicalised in prison, and was on a police watch-list.
His criminal record included convictions for armed robbery and drugs offences, Paris prosecutor Francois Molins told reporters late on Saturday.