Anti-terrorist investigators have been questioning the suspects mostly from Tunisia and Algeria, although some hold French nationality.
Police have four days before they must either release them or present them before a judge.
Some of those arrested are believed to have carried out armed robberies to raise funds for extremist groups.
Officials said others may have been involved in money-laundering via high-street businesses.
Police said they confiscated a number of weapons and other equipment.
The suspects had been under surveillance for several weeks and were detained after evidence emerged that “violent actions” were being planned, investigators said.
But it is unclear whether any targets had been contemplated.
One official close to the investigation said the group could have been
planning attacks on “highly symbolic targets” in France.
But another said its aim was to “finance the cause notably for the carrying out of terrorist attacks abroad.”
The main suspects were picked up at their homes in the Seine-Saint-Denis, Yvelines, Hauts-de-Seine, Val-de-Marne and Oise areas around dawn.
A number of Internet cafes were also raided.
Police scientists were at the scene of the arrests to check for traces of chemical, bacteriological or nuclear material.
Some of those arrested are “known to the authorities for possession of false papers and taking part in robberies,” and some have made journeys “in countries which are being watched by Western intelligence agencies,” officials said.
Others may have been planning to travel to Iraq or recruit volunteer
fighters to go there, they added.
The operation was carried out by members of the domestic intelligence service DST acting under the instructions of France’s leading anti-terrorist magistrate Jean-Louis Bruguiere.
France on alert
France stepped up its level of anti-terrorist alert after the July bombings in London, and government ministers have warned repeatedly that the country is seen as a target by Islamist militants.
Last month the French National Assembly approved an anti-terrorism bill that will permit increased video surveillance, give police wider access to telephone and computer data, and extend initial detention periods in terrorist cases from four to six days.