France’s prime minister, Michel Barnier, is facing a no-confidence vote that is very likely to topple him and his cabinet, leaving the country without a functioning government or a budget as it enters the new year.

Does that mean France is hurtling toward a constitutional crisis, or an American-style government shutdown in which civil servants are unpaid and departments are unfunded? Not exactly.

France’s Constitution offers several scenarios that could keep the country’s affairs more or less in order, at least in the short term. French institutions are relatively strong, and the country’s laws provide for continuity in the absence of a government and a budget.

But there is a price: Investors are already selling off French stocks and bonds, raising the country’s borrowing costs. And the political turmoil that has gripped France since President Emmanuel Macron called snap elections last summer is worsening.

In a television interview on Tuesday evening, Mr. Barnier held hopes that lawmakers would display “a reflex of responsibility” to keep his government alive, and he warned of rising interest rates and chaos if a budget isn’t passed.

“Everything will be more difficult and more serious,” he said.

Mr. Barnier and his government are facing two no-confidence motions that were filed this week after he pushed a budget bill through the lower house of Parliament without a final vote.

The two motions will be discussed and voted on Wednesday starting at 4 p.m. Paris time. One of those is almost certain to succeed.

To succeed, a no-confidence motion must get an absolute majority of votes — more than half of the total number of lawmakers elected to the lower house. The current threshold is 288 votes.

No party or bloc has enough votes to pass a no-confidence motion on its own. The lower house is divided into three main blocs: an alliance of left-wing parties called the New Popular Front, which has 192 seats; Marine Le Pen’s nationalist, anti-immigrant National Rally party and its allies, who hold 140 seats; and a tenuous coalition of centrists and conservatives who support Mr. Barnier, representing about 210 seats.

One of the motions against Mr. Barnier was filed by the New Popular Front, the other by the National Rally. The left has refused to support a no-confidence motion sponsored by the far right, meaning that the National Rally motion will likely fail.

But the National Rally says it has no qualms in supporting a left-wing motion, meaning that it is widely expected to get around 330 votes — more than enough to pass.

A successful no-confidence motion will topple the government. Mr. Barnier and the cabinet will be forced to resign, but not Mr. Macron. As a byproduct, the budget bill will also be rejected. If the no-confidence motion fails, the government and the budget bill will stand.

President Emmanuel Macron called snap elections last summer. The results were disastrous for his party and its allies. But instead of naming a politician from the leftist coalition that won the most seats in the election, Mr. Macron called on Mr. Barnier, a figure from the traditional centrist right. The leftist coalition was furious.

Since then, Mr. Barnier has been living “the hell of Matignon,” a phrase used by political commentators to describe the difficulties of reigning from Matignon Palace, seat of the government, where a prime minister has some power, but hardly all of it.

Mr. Barnier and his cabinet were appointed by Mr. Macron just three months ago. If they fall, they will become the most short-lived government in the history of France’s Fifth Republic, which was founded in 1958, and the first to fall to a no-confidence vote since 1962.

If the no-confidence vote passes, Mr. Barnier would have no choice but to resign, and the government would enter caretaker mode.

Mr. Macron’s previous government also drifted along in caretaker mode from July to September. It was empowered under the Constitution to handle “current affairs” but was limited in its powers.

No legal texts detail exactly what those limits are, but French jurists agree that a caretaker government can’t propose new laws or issue new decrees. It can take care of government business like paying workers and distributing pensions, for instance. The cabinet no longer meets.

It will then be up to Mr. Macron, once again, to appoint a new prime minister. He can take his time, and he can appoint whomever he likes — and not necessarily someone from the majority party in Parliament. He could reappoint Mr. Barnier, but in his interview on Tuesday, Mr. Barnier said he would refuse.

The budget itself would enter a kind of limbo. Without a functioning government, the budget proposed by Mr. Barnier, with around $60 billion of tax increases and spending cuts, would be dead on arrival. If Mr. Macron acts quickly and appoints a new prime minister before the end of the year, a new government budget could be submitted, and the Parliament would have 70 days to examine it.

But that would still mean France would not have a spending law by the new year. Under French law, the government could simply propose a “special measure” reapplying the 2024 budget, by Dec. 19. The civil servants would be paid and taxes would remain at their current level.

If Parliament refuses to go along or does not hold a vote, Mr. Macron could invoke his extraordinary constitutional powers and simply impose a budget. But jurists agree that the political consequences of such an untested move could be severe, especially at a time when the French president is increasingly challenged for failing to respect the voice of French voters.

Under France’s constitution, Mr. Macron will remain as president until his term expires in 2027, but it seems almost certain that his stature will be diminished. Some politicians on both the left and the right are calling for his resignation, but he has resisted those calls. His term is limited, and he cannot seek another stint in office.

Aurelien Breeden contributed reporting.