Two women were killed by a man armed with a knife at the main train station in the Mediterranean port city of Marseille on Sunday before being shot by soldiers patrolling there.
One of the victims had her throat slit by the assailant, a man with a criminal record believed to be in his 30s who witnesses said shouted "Allahu akbar" before attacking the women.
French interior minister Gerard Collomb said about a dozen witnesses were being questioned.
"This act could be terrorist in nature but at this time we cannot confirm that," he added.
Soldiers serving in a special 7,000-strong force known as Sentinelle set up to guard vulnerable areas of the country responded to the stabbings and shot dead the attacker, whose identity remains unknown.
"I was on the esplanade just in front of the station," said Melanie Petit, an 18-year-old student. "I heard someone shout 'Allahu akbar' and I saw a man who seemed to be dressed all in black."
Heavily armed police sealed off and evacuated the ornate rail terminus in the bustling heart of France's second-biggest city, stopping all train traffic on some of the country's busiest lines.
The latest deaths come with France still on high alert and under a state of emergency following a string of attacks in recent years by extremists linked to ISIL or Al Qaeda.
Since 2015, a total of 239 people have been killed in France by extremists, according to an AFP count before Sunday's incident.
After the attack, anti-terror prosecutors said they had opened an investigation into "killings linked to a terrorist organisation" and the "attempted killing of a public official".
Travellers around the station described "controlled panic" as security forces evacuated passengers and looked for possible accomplices, while another witness said white sheets were placed over the bodies of the victims.
"There were police everywhere," said Francois Jacquel, a retired traveller who was in a waiting room.
The incident came only days after ISIL released a recording of what it said was its leader, Abu Bakr Al Baghdadi, urging his followers to strike their enemies in the West.
