French Prime Minister Manuel Valls has warned of potential further attacks to France, and said that since the summer, French intelligence services had prevented five attacks.
Mr Valls said attacks are being prepared, not just against France but also against other European countries.
The Associated Press is reporting that senior Iraqi intelligence officials warned members of the US-led coalition fighting Islamic State of imminent assaults by IS just one day before the weekend's deadly attacks in Paris killed around 130 people.
Co-ordinated raids by anti-terrorism forces are taking place across France, according to local and international media reports.
Police are believed to have conducted at least 110 house searches in cities around France overnight.
The activity follows Friday's attacks in Paris, in which 132 people were killed and about 350 injured - with 97 of those in a critical condition. Islamic State has claimed responsibility for the attacks.
The attackers opened fire and used explosive devices at seven locations across Paris, including a concert hall, restaurants, bars and outside a stadium.
A huge manhunt is under way for surviving members and accomplices of the group.
The Guardian said it was hearing reports of pre-dawn raids today in Toulouse, Grenoble and Calais, while local Toulouse paper La Dépêche du Midi tweeted a photo of police vehicles involved in an 'anti-Islam' operation early on Monday morning.
Meanwhile, France's iTele reported that at least three people had been taken into police custody in Toulouse after what it called an anti-terrorism raid.
#Toulouse > Au moins 3 personnes ont été placées en garde à vue après perquisition conduite dans le cadre de la lutte antiterroriste— iTELE (@itele) November 16, 2015
Toulouse was the site of a terror attack in March 2012, when a series of gun attacks targeting Jewish civilians and French soldiers by terrorist Mohamed Merah saw seven killed and five injured.
France Info said that in addition to the three people taken into custody, police had seized a weapon, some cannabis and 'forbidden items' in Toulouse.
AFP reported that Bobigny, an outer suburb of Paris, had been raided late on Sunday night with several houses searched, but that the results of the raid were still unconfirmed.
A witness told the news organisation that police had interrogated local residents of the suburb.
In Jeumont, a French town close to the Belgian border, L'Observateur reported police began a large-scale operation around 1am close to the centre of town, with 20 police vehicles.
Fifty personnel and police officers closed off the roads around a single house, where a search was carried out, it said.
Le Dauphiné Libéré, a Grenoble local paper, said that in the latter part of the night, weapons and money were seized as a part of a large operation that began around 1am.
More than half a dozen people were arrested, it reported, some of whom were already known to police.
But there were no specifics on when and where the attacks would take place.
French police anti-terrorism units RAID (Recherche Assistance Intervention Dissuasion [Search, Help, Intervention, Deterrence]) and GIPN (Groupes d'Intervention de la Police Nationale [National Police Intervention Groups]) are the two tactical units reported to be involved in the police raids.