"France reiterates its strong disapproval of the indiscriminate fire of the Israeli army," French foreign ministry spokeswoman Agnes von der Muhll said in a statement. "All possible light must be shed on these serious events."
Israeli troops fired tear gas and live rounds at thousands of demonstrators on the second "Great March of Return" calling for the right of return for the families of the roughly 700,000 Palestinians who were driven out of or fled their homes when the state of Israel was created in 1948.
At least 491 Palestinians were wounded and nine people killed, including Mourtaja who was wearing a flak jacket with press markings.
On the previous demonstration on 30 March 17 Palestinians were killed.
On both occasions some protesters burnt tyres and threw stones and Molotov cocktails at the soldiers.
"France calls on the authorities concerned to exercise the utmost restraint and stresses that the use of force must be proportionate, in accordance with international humanitarian law to prevent further victims," the foreign ministry statement added.
Army promises to investigate journalist's death
The Israeli army has promised to investigate Murtaja's death but insisted that its troops only fired on "instigators".
Its troops are “operating in accordance with clear rules of engagement” and it does “not intentionally target journalists”, it added.
The Palestinian journalists' union says five reporters were injured on Friday.
Press freedom campaign Reporters Without Borders said Murtaja was "was obviously the victim of an intentional shot”.
“RSF condemns absolutely the deliberate shooting of journalists by the Israeli army," said secretary general Christophe Deloire on Twitter.
The Israeli journalists' union called for clarification on the Palestinain reporters hit by soldiers' fire in a letter to the Chief of Staff Gadi Eisenkot.
A group of 70 NGOs active in Gaza called for an "independent and transparent" inquiry into the "illegal murder of civilians in Gaza".
Israeli leaders were unrepentant, however.
Prime Minister Benjamin Netanyahu "saluted" the Israeli soldiers "who protect us at all times".
The protesters "talk about human rights but actually want to crush the Jewish state," he said. "We won't let them."
And Israeli Defence Minister Avigdor Lieberman said Sunday there were "no naive people" in Gaza.
"Everyone's connected to Hamas, everyone gets a salary from Hamas, and all the activists trying to challenge us and breach the border are Hamas military wing activists," he told Israeli public radio.
The demonstrations are planned to continue every Friday for the next six weeks.
Israel claims that Hamas, which controls the Gaza Strip, is exploiting the protests to carry out violent attacks on Israel.