The suspects, two men and a woman, were taken into custody Thursday in Paris and the suburban Val-de-Marne region, police officials said.
They were being held for questioning at the headquarters of French anti-terrorist police.
On Thursday, French authorities said a letter had been received from AZF claiming it was suspending its terror threats while it improves its ability to carry them out.
In excerpts from the letter published in the Paris daily newspaper Le Monde, AZF said it was suspending its activities in order to correct “technical problems.”
The letter carried the logo “AZF” with an arrow in the top left corner.
But the letter — addressed to President Jacques Chirac and Interior Minister NIcholas Sarkozy — warned that if the French government does not pay $4 million to AZF, the group will launch attacks worse than those in Spain.
“France will surpass without glory the sad Spanish records,” the letter said, an apparent reference to the March 11 bombings of four trains in Madrid which killed 190 people.
“So understand well that we in no way renounce obtaining the sum … that you should consider as a subsidy,” it said.