PARIS—French police detained five teenage boys for questioning in relation to the desecration of a Jewish cemetery in the eastern part of the country, an incident that has raised anxiety among French Jews about their security.

Philippe Vannier, a French state prosecutor in Saverne in the Alsace region, told a news conference on Monday that one teen had turned himself in, which then led the police to four others who are suspected of knocking over and vandalizing about 250 out of the 400 tombstones at the cemetery.

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