"France calls for a constructive national dialogue to engage in Iraq," Macron said at a joint news conference in Paris with Iraqi Kurdish leaders, including Prime Minister Nechirvan Barzani.
Baghdad and the Kurdish regional capital Arbil have been locked in dispute ever since September's independence referendum, which resulted in a resounding "yes" vote for independence in the autonomous Kurdish region of northern Iraq.
Iraqi security forces backed by paramilitaries responded by seizing the oil-rich Kurdish-held city of Kirkuk in October and other disputed territory.
Long-serving Kurdish president Masoud Barzani, whose nephew is Nechirvan, then resigned over the affair.
"Having a strong, reconciled, pluralistic Iraq which recognises each of its components is a condition for the immediate and medium-term stability," of the Middle East, said Macron.
The French president, who previously met Iraqi Prime Minister Haider al-Abadi on 29 October, said dialogue needed to be built in "full respect of the constitution of 2005".
He also called for "a gradual demilitarisation, in particular of the 'Popular Mobilisation' that has taken place in the last few years, and that all militias be gradually dismantled".
Fighters from Iraq's Hashed al-Shaabi are a controversial fighting force that formed in 2014 after the country's most revered Shiite cleric, Grand Ayatollah Ali al-Sistani, urged citizens to take up arms against Islamic State jihadists.
Bringing together a dizzying array of paramilitary groups under the command of Iraq's prime minister, the Hashed has since played a key role in battles against IS and more recently against Kurdish forces.
But the Shiite-dominated alliance remains deeply divisive; has often been described as an Iranian-backed group, and has been accused of a wave of abuses.
The French president said the new generation of Kurdish leaders has a "historic responsibility" and said France would do all it can to ensure "dialogue can succeed," indicating that he will soon meet Abadi again.
Nechirvan Barzani, who has been trying to negotiate an end to the confrontation with Baghdad, said on Saturday that his government "respected" a verdict by the Iraqi Supreme Federal Court that ruled the independence referendum unconstitutional.
He also said he had "no problem" with the federal government over the issue of border control.
The Iraqi federal government has demanded the handover of border posts and airports in the Kurdish region.