Agents from France's DCRI domestic intelligence agency swooped in to carry out the arrests, most of them in the southern city of Toulouse a day after Al-Qaeda-inspired gunman Mohamed Merah was buried there, sources close to the investigation said.
The arrests were "not directly linked" to the Merah investigation, but were aimed at dismantling Islamist networks, one source said.
Some of the arrests also targetted people in the western city of Nantes.
The arrests came a day after Merah, who was shot dead by a police sniper on March 22 at the end of a 32-hour siege at his flat in Toulouse, was buried in the city under heavy police watch.
The 23-year-old had shot dead three soldiers, and three children and a teacher at a Jewish school in a killing spree that shocked the country.
The man branded a "monster" by French leaders was laid to rest in Toulouse's Cornebarrieu cemetery after his family's homeland Algeria refused to accept the body, citing security concerns.
French authorities have charged Merah's brother Abdelkader with complicity in the attacks and said they were looking for other accomplices.
Abdelkader Merah was charged with helping his sibling steal the powerful Yamaha scooter used in the shootings and police have said they were seeking a third person who may have been involved in the theft.
Merah recorded his killings with a camera strapped to his body and police have said an accomplice may have been involved in mailing a montage of the videos to Al-Jazeera.
The video was reportedly sent to the channel's Paris bureau from outside Toulouse while Merah was already besieged in his flat by police.
French President Nicolas Sarkozy vowed a crackdown on Islamist extremists in the wake of the killings, saying earlier this week that he had ordered the domestic intelligence agency to "check in detail the situation in our country of all persons identified as a potential risk to national security".
On Thursday France banned four Muslim preachers from entering the country to attend an Islamic conference, saying their "calls for hatred and violence" were a threat to public order.
Saudi clerics Ayed Bin Abdallah al-Qarni and Abdallah Basfar, Egyptian cleric Safwat al-Hijazi and a former mufti of Jerusalem Akrama Sabri are banned from entering France, a statement said.
"These people's positions and statements calling for hatred and violence seriously damage republican principles and, in the current context, represent a serious threat to public order," said the statement from Foreign Minister Alain Juppé and Interior Minister Claude Guéant.