The graffiti appeared in the cemetery in Quatzenheim, near Strasbourg, overnight on Tuesday – hours before planned nationwide marches against a rise in antisemitic attacks.
French president Emmanuel Macron visited the graveyard on Tuesday, walking through a gate with a swastika sprayed onto it.
He paid his respects at one of the desecrated graves and told Jewish community members and local leaders: “It’s important for me to be here with you today.”
There were more than 500 antisemitic attacks across France in 2018, a 74% increase from 2017, figures released last week revealed.
After a series of antisemitic attacks last January Mr Macron urged the whole of France to “rise up” against “disgusting attacks” on the country’s Jewish community.
Incidents in recent days included yellow vest protesters on Saturday abusing Alain Finkielkraut, a well-known Jewish writer and son of a Holocaust survivor.
It has grown by about half since the Second World War, but antisemitic attacks remain common.
Earlier this month a bagel shop was sprayed with the word Juden – German for Jews – in yellow letters.
A Jewish cemetery in Herrlisheim, north of Strasbourg, also had many of its gravestones daubed with swastikas in December last year.
In 2015 four Jews in a Kosher supermarket in Paris were among 17 killed across the city by Islamist militants.
“These acts are disgusting,” Prime Minister Edouard Philippe told parliament last week.
“We need to educate and remind people about our history, to talk about the horrors that hide behind those criminal acts.
“We also need to punish (more) and we know that we can’t be hesitant on that.”
Mr Macron will host a dinner on Wednesday with the head of Crif, the overarching body that represents the Jewish community in France.