The damage was discovered on Tuesday morning at a cemetery in the village of Quatzenheim, close to the border with Germany in the Alsace region, a statement from the regional security office said.
It's just the latest shocking incident of anti-Semitism in France.
According to authorities around 80 graves in total were vandalised with anti-Semitic graffiti and swastika symbols.
Photos show the Nazi symbols in blue spray-painted on the damaged graves, one of which bears the words “Elsassisches Schwarzen Wolfe” (“Black Alsacian Wolves), a separatist group with links to neo-Nazis in the 1970s.
The top security official for the region, Jean-Luc Marx, condemned “in the strongest possible terms this awful anti-Semitic act and sends his complete support to the Jewish community which has been targeted again,” the statement added.
President Emmanuel Macron will travel to the cemetery to inspect the damage Tuesday, before visiting the Paris Holocaust memorial, Interior Minister Christophe Castaner told RTL radio.
Local MP Sylvain Waserman said he was left “disgusted” and “furious” after hearing of the vandalism.
The incident comes on the day mass rallies are planned in Paris and other French cities Tuesday to denounce a flare-up of anti-Semitic acts.
“This is the response to the national wake-up call we urged last week,” said Francis Kalifat of the CRIF umbrella group of French Jewish organisations.
He was referring to a spate of anti-Jewish vandalism and graffiti discovered in and around Paris in the days following another Saturday of yellow vest protests.
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Graffiti on the headquarters of French daily Le Monde used anti-Semitic tropes to refer to Macron's former job as a Rothschild investment banker.
In another incident, the words “Macron Jews' Bitch” was written in English across a garage door in the city centre, and the phrase “Jewish pig” was sprayed onto a wall in the northern 18th arrondissement.
But the rise in anti-Semitic acts in France predates the yellow vest movement.
Last year, police recorded a 74 percent surge in reported anti-Jewish offences, causing alarm in a country that is home to the biggest Jewish population in Europe.
The government has tried to walk a fine line in condemning the recent surge in anti-Semitism while not criticising what it calls the protesters' legitimate complaints.