French police have made two new arrests in the probe into an attack on a church in the southern city of Nice that left three dead, as authorities seek to understand the profile of the suspected killer, judicial sources said on Sunday.

Authorities are now holding a total of six people for questioning to understand if they were linked to Tunisian Brahim Issaoui, who prosecutors say carried out the knife rampage early Thursday morning in the Notre-Dame Basilica.

It so far remains unclear if he had outside help for the attack, which French President Emmanuel Macron has described as an act of "Islamist" terror and was the latest of a string of attacks in recent weeks in France.

The latest people to be detained are aged 25 and 63 and were arrested on Saturday at the residence of an individual detained earlier in the day, a judicial source told AFP, asking not to be named.

Three others detained earlier over suspected links to Issaoui remain in custody.

Issaoui was shot by police multiple times and is currently in a serious condition in hospital. Investigators have been unable to question him and his precise motivations remain unclear.

"It is still too early to say if there were others complicit, what his motivations were in coming to France and when this idea took root in him," another source close to the inquiry who asked not to be named said Saturday.

Tributes to victims of Nice church attack
People have left tributes to the victims of the Nice attack outside the church. Photo: AFP / Valery HACHE

The source said information from two telephones belonging to him and also an investigation being undertaken by the Tunisian authorities would be decisive in the probe.

Investigators believe Issaoui travelled illegally to Europe via Italy's Mediterranean island of Lampedusa on September 20.

He arrived at the mainland Italian port of Bari on October 9 before coming to Nice just two days before the attack.

France is on edge after the republication in early September of cartoons of the prophet Mohammed by the Charlie Hebdo weekly, which was followed by an attack outside its former offices, the beheading of a teacher and now the attack in Nice.

On Saturday, an attacker armed with a sawn-off shotgun seriously wounded a Greek Orthodox priest in a shooting outside a church in the French city of Lyon.

Nikolaos Kakavelaki, 52, was closing his Lyon church mid-afternoon when he was attacked and is now in a serious condition in hospital, said a police source who asked not to be named.

The attacker fled the scene but Lyon's public prosecutor later announced that a suspect had been arrested while adding that the motivation for the attack was not clear.

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