French President Emmanuel Macron began his latest search for a prime minister on Friday as the centre-left Socialists signalled they were open to joining a broad government coalition, sparking tensions inside an increasingly fragile leftwing bloc.

Macron this week rejected demands to resign to resolve France's political crisis, saying conservative prime minister Michel Barnier had been driven from office by the far right and extreme left's "anti-republican front".

"We came to say we want left-wing policies with a left-wing prime minister and that this is the message that he (Macron) now needs to understand after he picked Michel Barnier," Socialist Party chairman Olivier Faure said after meeting the president.

In a sign of shifting political tides, Faure said he was ready to back a broader government as "everyone could see" the current political gridlock was harming France, but added that he could not work with another rightwing prime minister "under any circumstance".

Seeking a way out of the political paralysis that followed snap elections this summer, Macron's allies tried for months to drive a wedge through the leftwing alliance known as the New Popular Front (NFP), urging the socialists to cut ties with the more radical France Unbowed (LFI).

LFI's firebrand leader Jean-Luc Melenchon slammed Faure for talking to the president, saying in a social media post: "Nothing of what he's doing is in our name or the name of the NFP."

In a prime time address on Thursday, Macron said he would announce a new prime minister in the coming days to replace Barnier, who was ousted in a no-confidence vote by lawmakers angered by his belt-tightening 2025 budget bill.

But it remains to be seen how Macron can cobble together enough support in parliament to pass the budget, or install a prime minister with any sort of longevity.

France's budget deficit has spiralled upwards this year, worrying financial markets, but the failure to agree a plan to rein it in has seen French borrowing costs jump higher still.

The Socialists, a moderate leftist grouping with 66 seats in the National Assembly, voted to topple Barnier this week, but could emerge as crucial kingmakers.

If Macron can win their backing, a new prime minister would likely have the numbers to stave off no-confidence motions from Marine Le Pen's far-right National Rally and other parts of the left.
Faure said that Macron should also seek to bring in the Greens and Communists.