The investigation concerns "damage committed on religious grounds", according to the authorities. No one has been arrested.
"I feel deep disgust towards these vile acts directed against the Jewish community", writes the country's interior minister Bruno Retailleau on X.
Last week, the minister called for "clear and deterrent" security measures at sites with Jewish connections due to concerns over possible anti-Semitic acts.
France's Jewish community is one of the world's largest. It has been hit by an increased number of desecrations of memorials since the Gaza war broke out on October 7, 2023.