Both groups are well known for driving vehicles into innocent people, prompting fears that tonight's incident could be linked to their activities.
Bastille Day, which celebrates the storming of the Bastille prison in Paris during the French Revolution of 1789, is the country's biggest public holiday.
At least 30 people were killed in the southern French town of Nice when a truck ran into a crowd celebrating the Bastille Day national holiday on Thursday night, French TV channel BFM TV said.
The truck rammed into the crowd on the Promenade des Anglais seaside walk in the centre of town, regional newspaper Nice Matin reported, citing its own reporter at the scene.
French television channel BFM TV said the local prefecture in Nice was treating the incident as an attack and was asking people to stay at home.


The southern French city of Nice was under terrorist attack tonight as 'dozens of people' were killed, and scores more injured during Bastille Day celebrations.
At least 50 people have been killed in the attack with reports of exchanges of gunfire between police and suspects.
A spokesman for the Alpes Maritime prefecture advised locals to 'stay indoors' as gunfire was heard, and a lorry was driven into a crowd on the Promenade des Anglais.
Eyewitnesses said there were 'bodies everywhere' with at least 100 people injured.