The investigation was opened at the request of Arafat's family after an examination of his personal effects commissioned by al-Jazeera found traces of polonium, Radio France Internationale reported.
A legal complaint against persons unknown was filed by Arafat's widow, Suha, and daughter, Zarwa, July 31.
French doctors have ruled Arafat had a blood condition known as disseminated intravascular coagulation and suffered a stroke leading to his death.
News of the police investigation was welcomed by the Palestinian Authority.
Saeb Erakat, a senior Palestinian official, said he hoped it would "reach the full truth on Arafat's death and who stands behind it."
Israel said it was not concerned about the French inquiry, Foreign Ministry spokesman Yigal Palmor said, "despite all the hare-brained allegations made against us."
Israel denies any involvement in Arafat's death.