"France expresses deep concerns over the serious incidents that have taken place recently in the Gaza Strip. France reminds Israeli authorities of their responsibility to protect civilians and calls on them to exercise maximal restraint," the statement said.
The ministry said that the Palestinians had the right to gather peacefully.
At the same time the Israeli side claimed that it had responded to violent actions of the Palestinians.
The Palestinian protest dubbed "The Great Return March" that started earlier in the week is dedicated to the so-called Land Day commemorating the day in 1976 when Israeli troops killed six Arabs protesting against confiscation of land.
The protest will reportedly last until May 15, when the Palestinians will commemorate the Nakba (disaster in Arabic), when hundreds of thousands of Palestinians were displaced after Israel announced its independence in 1948.