The raids come a week after gunman Mohammed Merah, who killed seven people, was shot dead after a long siege in the southwestern city of Toulouse.
The arrests took place in Toulouse, Marseille, Nantes, Lyon and the Ile de France region, around Paris, the Interior Ministry said.
Authorities have not said that any of those arrested were directly linked to Merah.
Sarkozy told Europe 1 that the decision to act had been taken by the interior minister and foreign minister "to deny the entry of certain people to France" who did not share the country's values.
"It's not just linked to Toulouse. It's all over the country. It's in connection with a form of radical Islam, and it's in agreement with the law," he said.
"What you have to understand is that the traumatic events in Montauban and Toulouse were profound in our country. I don't want to compare horrors but it's a bit like the form of trauma visible in the United States and New York after 9/11. We have to be able to draw some conclusions." Read More