"This whole story about Daesh is impossible for me, I don't want to hear it," his father Nureddine Hanachi, a retired former waiter at a Vienna hotel, told French news agency AFP, using an Arabic acronym for the Islamic State group.
"Maybe he was under the influence of drugs," when he carried out Sunday's attack on the two young cousins outside the main railway station of the city in southern France, said the man in his 60s at the family home in a middle-class district near Zarzouna, around 70 kilometres (45 miles) north of Tunis.
The father said the IS claim of responsibility for the attack was "a lie" and nothing more, while an uncle said 29-year-old Ahmed "enjoyed the good life", and would never have got involved with jihadists.
IS's propaganda agency Amaq claimed the killer was one of its "soldiers", although a source close to the investigation has told AFP no solid evidence linked him to the group.
Witnesses to the attack heard the assailant shout "Allahu Akbar" (God is greatest) as he lunged at the women with a 20-centimetre (eight-inch) knife before threatening soldiers, who shot him dead.
Friends back home, like the family, find it hard to associate Hanachi, whom they remember as a partygoer and heavy user of drugs and alcohol, with IS.
"This was someone who, as soon as he opened his eyes in the morning, said: 'Let's go for a drink'," said Anwar, 29.