Bayrou has flagged the September 8 vote over his plans for sweeping budget cuts.
The far-right National Rally, the Greens and later the Socialists, on whose vote Bayrou's fate largely lies, said they did not see how they could back him.
If he loses the confidence vote in the National Assembly, Bayrou's government will fall.
The uncertainty spooked investors, pushing the risk premium on French bonds over their German equivalents up 5.0 basis points to their highest level since mid-June.
The CAC-40 index of leading French shares ended the day down 1.6 per cent.
If the government falls, President Emmanuel Macron could name a new prime minister immediately or ask Bayrou to stay on as head of a caretaker government, or he could call a snap election.
Macron lost his last prime minister, Michel Barnier, to a no-confidence vote over the budget in late 2024, after just three months in office following another snap election in July that year.
Bayrou acknowledged seeking the confidence of a very fragmented parliament was a risky bet.
"Yes, it's risky, but it's even riskier not to do anything," he told a press conference, referring to what he said was the major danger the country faced due to its huge debt pile.
The confidence vote, he said, would gauge whether he had enough support in parliament for his 44 billion euro ($A79.39 billion) budget squeeze, as he tries to tame a deficit that hit 5.8 per cent of gross domestic product last year, nearly double the official EU limit of 3.0 per cent.
Even if the government wins the confidence vote, it would only mean he has support for his views on France's fiscal woes, with a vote on the actual budget itself due later in the year.
Bayrou has proposed scrapping two public holidays and freezing welfare spending and tax brackets in 2026 at 2025 levels, not adjusting them for inflation.
He said his proposal to scrap the bank holidays could be tweaked.
Far-right party chief Jordan Bardella said Bayrou had de facto announced "the end of his government" by calling for the vote.
"The RN will never vote in favour of a government whose decisions are making the French people suffer," he said on X.
Leader Marine Le Pen said the RN would vote against Bayrou - as did the Greens.
The hard left France Unbowed also said the vote would mark the end of the government.
The votes of Socialist politicians will be decisive for Bayrou's fate because if they join other left-wing parties and the far right in voting against the government, there will likely be enough votes to oust it.
Socialist party leader Olivier Faure told TF1 television that French Socialists would not vote in favour of a confidence motion for Bayrou.
The confidence vote will take place just two days before planned protests, which have been called for on social media and backed by leftist parties and some unions.
The September 10 call for general protests has drawn comparisons to the Yellow Vest protests that erupted in 2018 over fuel price hikes and the high cost of living.
The "gilets jaunes" protests spiralled into a broader movement against Macron and his efforts at economic reform.
