French President Emmanuel Macron has come under pressure to name a new prime minister quickly after François Bayrou lost a vote of no confidence and on Tuesday handed him his resignation.

The fall of Bayrou’s government came as no surprise, because a majority in France’s hung parliament staunchly opposed Bayrou’s bid to bring down France’s spiralling debt with €44bn (£38bn) budget cuts.

But Macron is still faced with one of the highest budget deficits in the eurozone and mounting criticism from political opponents.

France is also facing a day of protests on Wednesday from a nebulous grassroots movement called Bloquons Tout – “Let’s Block Everything”, and authorities are planning to deploy 80,000 police.

As Monday’s confidence vote was called by Bayrou himself, Macron has had weeks to prepare his next step. He has already made clear he will choose a new prime minister in the coming days – the fifth since he won a second term as president in 2022.

Whoever the president ends up choosing will be in the unenviable position of having to face a hung parliament split into three factions deeply at odds with one another.

None has a majority and several are clamouring for fresh elections instead of a new prime minister.

Speculation over potential frontrunners began swirling even before Bayrou’s government fell, with names from Assembly speaker Yaël Braun-Pivet to current defence minister Sébastien Lecornu being floated.

However, commentators believe Macron will need support from the left or centre-left camp to ensure support from the Socialists and the centrists and give the new prime minister a fighting chance of passing a much-needed budget tackling France’s debt.

Macron ally and ex-prime minister Gabriel Attal has deplored the “state of permanent instability” plaguing France and urged Macron to find a technocrat “negotiator” to find common ground between political leaders together before naming a prime minister.

Attal’s suggestion was immediately rubbished as “total nonsense” by Marine Le Pen of the far-right National Rally who is among those calling for fresh parliamentary elections.

But a new vote at this stage was implicitly rejected by Macron promising a new prime minister would be announced “in a matter of days”.

His statement reflected an urgent need for France to regain some stability as the country faces market jitters, protests and large-scale industrial action.

Authorities are bracing for nationwide disruption on Wednesday, with the Bloquons Tout movement urging citizens to bring the country to a standstill through protest and acts of civil disobedience against “austerity, contempt and humiliation”.

Although it is unclear how many people will heed the group’s call, on Tuesday right-wing interior minister Bruno Retailleau acknowledged 100,000 could take part across France and promised to mobilise police to face “organised and seasoned groups who seek violence”.

More co-ordinated action is expected next week. Trade unions have called a strike to protest the government’s “brutal” budget plans, lamenting that France “has been sinking into a profound social and democratic crisis”.

Blaming the radical left headed by Jean-Luc Mélenchon for creating an “insurrectionist mood”, Bruno Retailleau warned that September “could lead to all kinds of excesses”.

France is also bracing for a decision on Friday from credit agency Fitch, which could see its rating demoted and make it more costly to borrow money. France’s public debt rose to €3.3tn earlier this year, which is 114% of its economic output or GDP.

“We need a prime minister to embody power – and very quickly,” said Retailleau. “It’s crucial, including in terms of maintaining order.”

On Tuesday morning Paris police chief Laurent Nuñez said pig heads had been found outside nine mosques in the region. Pigs are considered by Muslims to be impure, and Paris Mayor Anne Hidalgo denounced the incidents as “racist acts”.

Nuñez said he “couldn’t help but make a link” with previous incidents which were later proven to have been “acts of foreign interference”.

“An action of such magnitude, carried out simultaneously by several people, raises questions,” he said.