The daubing of swastikas and other anti-Semitic graffiti on the graves at the cemetery in Westhoffen around 15 miles west of Strasbourg in the Alsace region was the latest racist attack to shock the country.
"Jews are and make France," President Emmanuel Macron wrote on Twitter on Tuesday.
"Those who attack them, even their graves, are not worthy of the idea we have of France."
"Anti-Semitism is a crime and we will fight it in Westhoffen as everywhere until our dead can sleep in peace," he added.
In response to the latest in a string of such acts of anti-Semitic vandalism, France is to open a national bureau to lead the fight against hate crimes.
The office, which would be part of France's gendarmerie, will be charged with investigating this crime but also all anti-Semitic, anti-Muslim and anti-Christian acts, said interior minister Christophe Castaner.
"The Republic itself has been desecrated," said Mr Castaner said after visiting the cemetery, which dates from the 16th century.
The Alsace region has suffered a rash of racist vandalism over the past year, most notably the desecration of 96 tombs at a cemetery in Quatzenheim in February, which sparked nationwide outrage.
The rising number of anti-Jewish offences reported to police - up 74 percent in 2018 from the previous year - has caused alarm in the country that is home to both the biggest Jewish and the biggest Muslim communities in Europe.
Earlier this year, politicians from across the spectrum joined marches against anti-Semitism amid fears of a rise around the continent.
They denounced a surge in attacks that some commentators blamed on incitement by Islamist preachers, others on the rise of anti-Zionism - opposition to the existence of Israel as a homeland for the Jewish people.
The graves were desecrated just hours before French MPs adopted a resolution equating anti-Zionism with anti-Semitism.
On Tuesday evening, French MPs approved a non-legally binding resolution modelled on the definition of anti-Semitism set by the International Holocaust Remembrance Alliance (IHRA).
The IHRA definition, which serves as an international guideline, does not reference “anti-Zionism” but does say denying Jews their right to self-determination is anti-Semitic.
The World Jewish Congress hailed France’s step.
“For too long too many have used the excuse that their obsessive criticism of Israel stands exclusive from their otherwise positive feelings for the Jewish people. Those days are now over,” it said.
Debate over the resolution split Mr Macron’s ruling La Republique En Marche party, with some opponents saying it could smother freedom of expression in criticising the Israeli government.
Backers said it merely targeted those who refused to recognise the existence of Israel or sought its destruction.