Le Figaro, which published the commentary, said the teacher also was identified as a potential target on Islamist chat rooms.
Robert Redeker was placed under police surveillance last weekend following the September 19 publication of the opinion piece in which he accused Muslim fundamentalists of trying to muzzle Europe's democratic liberties.
Redeker, a high school philosophy teacher, said he had since received threatening e-mails, some containing photos of him, a map of his home and his telephone numbers, and has been named as a target by contributors to online Islamist chat rooms.
One e-mail read: "You will never again be safe on this earth. One billion, 300 million Muslims are ready to kill you," he told Europe-1 radio on Friday.
"I can't work, I can't come and go and am obliged to hide myself," he said. "I am constantly protected by security forces ... and am forced to change houses every two days."
The special anti-terrorism section of the prosecutor's office opened a preliminary investigation to be led by the DST, the counter-terrorism and counter-intelligence agency, judicial officials said.
Dominique de Villepin, the French prime minister, called for vigilance so that "respect for the opinions of others is total".
"We are in a democracy," Villepin said on RMC radio. "Each person should be able to express himself freely while respecting others."
Redeker called his situation "a little victory" for Muslim fundamentalists, saying they "succeeded in punishing me on French territory as if I was guilty of a speech crime".
He called on moderate French Muslims to support him.
"We must distinguish between Islamists and those responsible Muslims out there who should without a doubt support me," he said.