French police say they have arrested five teenagers over the desecration of hundreds of graves at a Jewish cemetery in Sarre-Union, a small town near the German border.

Local prosecutor Philippe Vannier said the suspects, aged between 15 and 17, are all males from the area who do not have a criminal record.

Vannier said the group were not known to hold any ideological beliefs that could have explained the act of vandalism.

One of the alleged vandals handed himself in to police, also reporting the names of his accomplices.

The boy denied he acted out of anti-Semitic hatred, Vannier said, adding that the five claimed "they believed it was an abandoned cemetery."

"[They claimed] to have realised that some of the graves were Jewish upon wrecking them," he said.

Nevertheless they are facing charges of religion-motivated grave profanation and group vandalism, which carry sentences of up to seven years in jail.

Authorities didn't release the names of the suspects.

Some 300 tombstones were defaced, knocked over or smashed at the weekend, leaving the graveyard "in ruins", according to local Jewish community representative Jacques Wolff.

The desecration was discovered hours after a 37-year-old Jewish security guard was shot dead outside a Copenhagen synagogue by a gunman who had earlier attacked a freedom of speech event in the Danish capital, killing another man.

President Francois Hollande had vowed to bring the vandals to justice, describing the incident as an "odious and barbaric" attack on French values. He plans to visit the cemetery on February 17

"France is determined to fight relentlessly against anti-Semitism and those who want to undermine the values of the Republic," Hollande said.

The desecration also fuelled a spat between Israeli Prime Minister Benjamin Netanyahu and his French counterpart, Manuel Valls, after the former called on European Jews to leave en masse for Israel.

"My message to French Jews is the following," Valls told RTL radio. "Like you, France is also hurt and it doesn't want you to leave. She [France] repeats once again her love, support and solidarity.

"Every Jew who leaves is a piece of France that goes away."

Anti-Semitic attacks in France, which is home to Europe's largest Jewish community, more than doubled in 2014, with some 851 incidents reported, according to the Council of Jewish Institutions in France (CRIF).

The Sarre-Union cemetery has been targeted by vandals twice in the past, with dozens of graves being damaged in 1988 and 2001.