In addition to the note near the body of 39-year-old Frenchman Karim Cheurfi, authorities found a Koran in his vehicle at the scene of Thursday's attack, the sources told AFP.
After killing the officer and injuring two of his colleagues just a few hundred metres (feet) from the Arc de Triomphe, the gunman was shot dead in return fire while trying to flee on foot.
A statement by ISIS's propaganda agency Amaq said the attacker was one of its "fighters", identifying him as "Abu Yussef the Belgian".
The killer identified by French authorities was known to anti-terror police, sources told AFP. He had been arrested in February on suspicion of plotting to kill police officers but released for lack of evidence.
He had been convicted in 2005 on three counts of attempted murder, including two targeting police officers, sources said. Police were questioning three people from his entourage.