French President Emmanuel Macron said he will name a new prime minister "in the coming days" after Michel Barnier resigned following a no-confidence vote in parliament.

In a 10-minute address to the nation on Thursday, he rejected opposition pressure to stand down, vowing to stay in his post "fully, until the end of the mandate" in 2027.

He thanked Barnier for his dedication during his brief term as prime minister and accused the French far right and hard left of collaborating in an "anti-republican front" to bring down the government.

French MPs voted overwhelmingly to remove Barnier on Wednesday, just three months after he was appointed by Macron.

The vote was the first time a French government had been voted down by parliament in more than 60 years, a move Macron labelled "unprecedented".

In response, Marine Le Pen, leader of the far-right National Rally (RN), posted to social media: "A little reminder to President Macron, who is supposed to be the guarantor of the Constitution: censure is not anti-republican, it is provided for in the Constitution of our Fifth Republic."

The no-confidence vote that toppled Barnier's leadership had been tabled by both the New Popular Front (NFP) left-wing alliance and Le Pen's RN.

They united to censure the government after the former Brexit negotiator used special powers to force through his budget without a vote.

A total of 331 MPs voted in support of the motion against Barnier, far more than the 288 required for it to pass.

Barnier resigned on Thursday, and the budget was automatically withdrawn. He will remain in office on a caretaker basis with his ministers until a new government is appointed. Macron's role is unaffected.

Macron has been heavily criticised for deciding to call snap elections in July, creating a deadlock in parliament and an escalating political crisis.

He admitted the decision he took "was not understood", saying: "Many have blamed me for it and I know, many continue to blame me. It's a fact and it's my responsibility."

Addressing voters directly, he said some of his political opponents had chosen "chaos over responsibility" and that they were not thinking "about you, the voters", suggesting their focus was on the next presidential elections.

Macron gave no indication of who the next prime minister would be, but said their immediate focus would be the budget for 2025.

Speculation has been swirling over who could be named, with potential candidates including Defence Minister Sébastien Lecornu, Interior Minister Bruno Retailleau, and centrist former presidential candidate François Bayrou.

But finding someone who would be supported by the majority of factions within the stalemate parliament could be difficult, as was the case when former PM Gabriel Attal was asked to stay on as caretaker for two months after July's elections.

It is unclear if the next government will now be in place before Saturday, when world leaders including US President-elect Donald Trump are due to attend the opening ceremony of the rebuilt Notre Dame Cathedral in Paris.

The building was devastated by fire in April 2019, and its reconstruction a little more than five years later has drawn worldwide praise.

Macron said the rebuilding of the ravaged cathedral, plus France's successful hosting of the 2024 Olympics, were "proof that we can do great things".

"We can do the impossible," he said. "The world admires us for that."