French authorities have made eight new arrests in connection with the Bastille Day truck attack in Nice that left 86 people dead, the Paris prosecutor's office said.

The office said the suspects detained on Monday were French and Tunisian and had links to the attacker, Mohamed Lahouaiej Bouhlel, who ploughed a 19-ton truck down Nice's Promenade des Anglais and into a crowd assembled for a July 14 fireworks display.

All eight were arrested in the Alpes-Maritimes region in the south-eastern corner of France that includes Nice.

At least five people already face preliminary terrorism charges in the attack, and are accused of helping Bouhlel obtain a pistol and providing other support. It was not immediately clear what the men arrested this week are suspected of.

The Islamic State group has claimed responsibility for the July 14 attack. French authorities say Bouhlel, a Tunisian with French residency, was inspired by the extremist group's propaganda, but they say no evidence has been found that IS orchestrated the attack.

France remains under a state of emergency after the Nice killings and IS attacks on Paris last year.

Interior Minister Bernard Cazeneuve said on Tuesday that the threat to France is higher than ever. He said about 300 people have been arrested in investigations into extremist networks so far this year, according to his office.

Also on Tuesday, authorities detained two boys, aged 14 and 17, in an investigation into a hoax hostage alert at a Paris church, the prosecutor's office said.

The false alarm on Saturday prompted a big police deployment and activation of an app-based terrorism alert system. A 16-year-old detained on Monday remains in custody.

The government is seeking financial compensation from the perpetrators for wasting security services' time and money, and scaring the public unnecessarily.

Obs magazine reported it was a case of "swatting", where hoaxers make anonymous threats to trigger a response from police and Swat teams.