The French fascination with the guillotine has found a new focus over the last week. The man under the knife is France’s silver-haired prime minister, Michel Barnier, known for composure on previous scaffolds.

His political life could even be over this week, or possibly before Christmas, a prospect prompting ghoulish speculation about financial chaos, American-style government shutdown and unpaid salaries for the fifth of France’s work force on the public payrolls. That the country might soon be without a government is adding to the French malaise — a soup of industrial layoffs, strikes, demonstrating farmers, anemic growth and a yawning deficit.

The prospect of a government collapse sent French borrowing costs soaring relative to Germany’s last week, pushing them almost to the level of Greece’s. A showdown could come as early as Monday, when Mr. Barnier might try to force through a budget bill on government health care and other social spending.

Even Mr. Barnier, a veteran politician who negotiated a tough Brexit deal for the European Union and served four times as a minister in previous governments, concedes that he is living on borrowed time. The woman in control of the blade is Marine Le Pen, leader of the far-right populist National Rally, which has more seats in the lower house of the French Parliament than any other party.

She doesn’t like Mr. Barnier’s budget of some $60 billion in tax increases and spending cuts. She doesn’t like his cuts to some medical reimbursements and increases in electricity fees — “violent, unjust, inefficient,” she told reporters on Tuesday — and she has suggested that her party will censure him if he forces his budgets through without a vote in Parliament. Mr. Barnier gave ground on the electricity fees on Thursday, but Ms. Le Pen said that was not enough.

Bypassing the lower house of Parliament — a French oddity, permitted under the Constitution — often provokes cries of autocracy and outrage among lawmakers. Led by the left, and joined by the far right, they will almost definitely put the government to a confidence vote.