Shooting has broken out around the Porte de Vincennes in Paris, Agence France-Presse has reported.
Reports from the agency and Le Figaro newspaper suggest an armed man took a hostage at a kosher deli nearby.
About 7,000 French Jewish people left the country last year and have moved to Israel because they did not feel safe.
The aunt of a man killed while trying to overpower gunman Amedy Coulibaly has told ITV News her family is fearful of their future in France.
A Muslim cleric in Pakistan has held a ceremony to honour Cherif and Said Kouachi, the two men suspected of the Charlie Hebdo massacre.