The letter from the group calling itself the “Servants of Allah the Mighty and the Wise” was addressed to the head of the French government and published in the Paris daily “Le Parisien.”
It was signed with the name “Commando Movsar Barayev,” on behalf of the shadowy group, the newspaper said.
Movsar Barayev is the name of the Chechen rebel and alleged leader of a deadly hostage-taking raid October 2002 on a theater in Moscow.
Russian special forces stormed the theater and killed Barayev.
The French Justice Department opened the investigation in conjunction with special police services.
Interior Ministry Nicolas Sarkozy said the letter is being analyzed.
Investigators said they had not heard of the group.
According to the Ministry of Justice, the letter contained “menacing threats for the entire nation…”
The threat was revealed as French President Jacques Chirac pledged to step up the fight against terrorism to protect citizens and institutions.
“Europe must always fight terrorism with all its strength,” Chirac told reporters.
German Chancellor Gerhard Schroeder, appearing with Chirac after bilateral talks in Paris, said he agreed with that assessment.