"Yesterday, I spoke with the Iraqi prime minister, Mohammed Shia al-Sudani," Macron said on X, writing in French and Arabic.
"I thank him for his commitment to getting to the bottom of this attack and to strengthening measures to protect our forces, who are present in Iraq to fight, alongside the Iraqis, against the scourge of terrorism."
Arnaud Frion, 42, was killed and six other French soldiers were wounded on Thursday evening in a drone attack in the Erbil region of Iraqi Kurdistan. He is the first French soldier to die since the start of the war in the Middle East.
"We will continue our coordination and our efforts to promote the country's stability and sovereignty, as well as regional de-escalation," Macron said.
Iraq's prime minister has vowed to prevent further attacks after Frion's death.
Macron has condemned the attack as unacceptable, but reaffirmed France's "purely defensive" stance in the conflict.
He refrained from attributing the attack, carried out by an Iranian-designed drone, to any specific group or country, or from mentioning a possible retaliation.
Without directly claiming responsibility for the strike, a pro-Iranian armed group in Iraq said on Friday it would target French interests in the region.
Soldiers from several countries, including Italy and France, are training members of the Kurdish security forces in Iraqi Kurdistan as part of the anti-jihadist coalition led by Washington.
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