French President Emmanuel Macron is seeking his fifth prime minister in less than two years after opposition parties united to oust centre-right Prime Minister Francois Bayrou over his unpopular plans for budget tightening.

Bayrou, handed a 364-194 defeat in a parliamentary confidence vote on Monday, will officially hand in his resignation to Macron on Tuesday.

Whoever Macron picks to succeed him will face the near impossible task of uniting parliament and finding ways to get a budget for next year adopted. France is under pressure to lower a deficit that stands at nearly double the European Union's 3% ceiling, and a debt pile equivalent to 114% of GDP.

Defence Minister Sebastien Lecornu's name was among those circulating for the next prime minister, with Macron's other options being to pick someone from the centre-left, or a technocrat.

There are no rules governing who the president should choose, or how fast. Macron, 47 and in office since 2017, will appoint his new prime minister in the next few days, his office said on Monday.

The Socialists were among those saying it was their turn to govern. "I would like it to be the left, the greens. We need to claim power," Socialist Party chief Olivier Faure told France Inter radio.

The far-right National Rally meanwhile repeated its call for a snap parliamentary election, which Macron has so far ruled out. Dissolving parliament "is the only way, the best way, to get out of a political crisis," party leader Marine Le Pen told reporters.

Macron's decision last year to call a snap parliamentary election only resulted in a more fragmented parliament.

Market reaction was relatively muted in early trading on Tuesday, with Bayrou's departure already largely priced in. The next test will be Fitch's decision on France's sovereign rating on Friday.