An official account states that the man, identified by a judicial source soon after the attack as of Moroccan origin, shouted Allahu Akbar (God is the greatest) and was wearing what turned out to be a fake suicide belt.
Molins told a French radio station that the man may have provided police with a false identity a few months ago.
He also said a cell phone found on the body was examined and contained a German SIM card.
“I’m not at all sure the identity he gave was real,” Molins told France Inter on radio on Friday.
A judicial source said Thursday that the dead man was Ali Sallah, a Moroccan born in 1995 in Casablanca.
He was homeless and was known to police for theft in 2012 in the Var region of southern France.
Molins said authorities determined from fingerprints that the dead man identified himself as Sallah to police when they intercepted him last year.
The name Ali Sallah was not known to the intelligence services.
Molins said a sheet of paper found on the man’s body gave him a different name and a Tunisian nationality.
A French police source on Friday said a relative of a Tunisian man, Tarek Belkacem, had identified him as the assailant on Thursday after seeing his photo on television and calling police from Tunisia.
“It’s a serious lead, but checks are underway to see if it’s really this person,” the source said.
He added that the man in question was of Tunisian nationality and had emigrated to France.
On the sheet there was also the flag of the Islamic State and a claim of loyalty to the militant group written in Arabic.
The Islamic State, which controls Swathes of Iraq and Syria, claimed responsibility for an attack in Paris on November 13 that killed 130 people.
Molins said counter-terrorism authorities are working on 215 cases involving 711 people in France.
About 240 people had been questioned in relation to them.