France's new prime minister resigned on Monday after less than a month in office, sinking the country further into a political crisis and dealing a fresh blow to President Emmanuel Macron.

"Mr Sebastien Lecornu has submitted the resignation of his government to the president of the republic [Macron], which he accepted," the French presidency said in a terse statement.

Lecornu's stint in office was the shortest ever for a prime minister in modern France.

His resignation compounds a political crisis that has rocked France for over a year, after Macron called legislative elections in the summer of 2024 that ended in a hung parliament.

The shock move appears to have been forced by the reaction of the right-wing Republicans to Lecornu's cabinet announced late on Sunday, which led the party to consider its future in the government.

It was not immediately clear how Macron would proceed. Up to now, he has resisted calls to again order new snap legislative polls and has also ruled out resigning himself before his mandate ends in 2027.

The 2027 presidential elections are expected to be a historic crossroads in French politics, with the French far-right under Marine Le Pen sensing its best ever chance of taking power.

"In the coming weeks there will be new [legislative] polls," predicted the leader of Le Pen's far-right National Rally (RN) Jordan Bardella. "The RN will obviously be ready to govern."

Macron named Lecornu, a former defence minister and close confidant known for his discretion and loyalty, to the post on September 9.

But the largely unchanged cabinet he unveiled late on Sunday sparked fierce criticism across the political spectrum.

The Republicans were not going to offer Macron and his allies "a final lap" after the largely unchanged cabinet, the right-wing party's vice-president Francois-Xavier Bellamy said.

The lineup included former long-serving finance minister Bruno Le Maire as defence minister.

Lecornu had faced the daunting task of finding approval in a deeply divided parliament for an austerity budget for next year.

Lecornu's two immediate predecessors, Francois Bayrou and Michel Barnier, were ousted by the legislative chamber in a standoff over the spending plan.

France's public debt has reached a record high, official data showed last week.

France's debt-to-GDP ratio is now the European Union's third-highest after Greece and Italy, and is close to twice the 60 percent permitted under EU rules.

Previous governments had rammed the last three annual budgets through parliament without a vote, a method allowed by the constitution but deeply criticised by the opposition.

But Lecornu promised last week to ensure lawmakers were able to vote on the bill. (AFP)