French President Emmanuel Macron on Tuesday gathered leaders of all parties – except the far right and the far left – for talks about forming a government, the first time under the hung parliament left by June's election that mainstream parties had sat down together.

The meeting included moderate left-wing leaders willing to compromise to break the political impasse, distancing themselves from the anti-capitalist France Unbowed, which declined to join them.

The centre-left Socialists are seen as likely kingmakers in Macron's bid to form a new government, with sufficient parliamentary support to make sure it survives, unlike the last cabinet under veteran conservative Michel Barnier.

"We have come to say we are ready to have a left-wing prime minister, but one who is open to compromise," Socialist Party leader Olivier Faure told reporters on his way into the Winter Garden of the president's Elysee Palace.

The Socialists, while sticking to their calls for a new prime minister to hail from the left, have shifted since Barnier's government was toppled in a vote of no-confidence last week.

In particular, they no longer insist on Macron naming a prime minister whom France Unbowed would approve of, saying France cannot remain rudderless.

A source in Macron's entourage declined to say whether he would indeed name a prime minister from the left, but did say entrenched positions had begun to shift.

The Socialists say Macron's decision not to invite Marine Le Pen's far-right National Rally (RN) opens space for cooperation. But Green leader Marine Tondelier said the president would also have to compromise, adding "We've come to hear what concessions Macron is willing to make".

Le Pen said she had not wanted an invitation.

"The president knows that, so he didn't invite the RN to the party where the jobs will be divided up." (Reuters)