To make the deal work, PSA will have to navigate elected officials and labor leaders in three countries where it has big plants — Britain, France and Germany. The focus of the deal has already been centered on saving jobs. In a conversation on Sunday with Mary T. Barra, the chief executive of General Motors, the British prime minister emphasized the need to protect the plants and the homegrown brand, Vauxhall.
Car companies provide particularly fertile ground for nationalist appeals. The closing of a car factory is often devastating for the surrounding community, and it can fall hardest on less-educated, lower-income workers who feel neglected by elites and victimized by global finance.
And car manufacturers are often entangled with national identity. Opel, which has belonged to G.M. since 1929, is based in Rüsselsheim, near Frankfurt, and it is widely perceived as a German brand. PSA, the maker of Peugeot and Citroën cars, is 14 percent owned by the French government.
“What better industry to express a view of ‘France first’ than the auto industry?” said David J. Herman, who was chief executive of Opel in the 1990s. Making the acquisition work, he said, “is going to be excruciatingly difficult.”
In France, Marine Le Pen of the far-right National Front has an outside chance at winning the presidency in May. Ms. Le Pen has sought in her campaign to capitalize on high unemployment, calling for “targeted protectionism” and “economic patriotism” for French companies.
In Germany, which will hold elections in September, Frauke Petry and her Alternative for Germany party are trying to win at least 5 percent of the vote, the threshold to seat a delegation in Parliament. Ms. Petry’s party has tried to cast the sale of Opel in nationalist terms. Last month, Paul Hampel, a member of Alternative for Germany’s national governing board, called the deal a “sellout of German know-how.”
At a time when European unity is under threat, the sale of Opel to PSA could strain relations among Britain, France and Germany as they try to ensure that any pain is imposed in someone else’s backyard. PSA’s Peugeot and Citroën factories are concentrated in France, while the biggest Opel and Vauxhall factories are in Germany and Britain.
It is difficult to see how PSA’s takeover of Opel, which would create the second-largest carmaker in Europe after Volkswagen, could succeed without major job cuts and, probably, shutting some factories. Opel has not been profitable since the 1990s, and both companies have more factories than they need. Unused factory space is deadly to a car company’s bottom line because it requires expensive upkeep without producing revenue.
“The idea is that this deal makes a strong second to VW,” Mr. Herman said, “but they’ve got to make money.”
The two British plants, with the Opel and Vauxhall brands, could be particularly vulnerable to political and economic forces. Britain’s vote to exit the European Union means that cars exported to the Continent could face substantial tariffs.
“Tavares is talking about saving $2 billion,” said Peter Wells, an automotive expert at Cardiff University in Wales, referring to the chairman of the managing board of PSA, Carlos Tavares. “It has to come from somewhere.”
The pressure on automakers had made the industry a point of contention in the discussion over a so-called Brexit.
Mrs. May, the prime minister, made undisclosed concessions to persuade Nissan to agree to build two new vehicles at its factory in Sunderland, England. Labor unions are preparing to try to block Ford from making threatened job cuts at an engine plant at Bridgend, Wales.
“The uncertainty caused by Brexit is harming the U.K. auto sector,” said Len McCluskey, general secretary of the union Unite, which represents many British autoworkers. “We need assistance from the government to give this sector a fighting chance.”
Such cases have prompted Mrs. May to speak of an industrial policy, repudiating years of Conservative Party free-market doctrine.
In January, the prime minister announced “a modern industrial strategy” as part of her plan to prepare Britain for a future outside the European Union. The government will no longer be laissez-faire, she said, but will be “stepping up to a new, active role that backs business.”
The French government has backed PSA’s acquisition of Opel, a bright spot in an otherwise gloomy economy. President François Hollande commended the alliance on Monday as the “birth of a European champion of the automotive industry.”
The deal represents a remarkable turnaround for PSA, which had a record loss just four years ago. Freed of constraints imposed by G.M., Opel may be able to establish a stronger presence in Asia and South America, potentially allowing the company to reduce its heavy reliance on the slow-growing European market.
But Opel will require work. In a reflection of the troubles, G.M. is selling its European operations for just $2.3 billion, and it is taking a charge of up to $4.5 billion as it books a paper loss from the deal. (PSA is spending about $1.85 billion, with BNP Paribas kicking in the rest in exchange for part of the financial group.)
“We think, with humility, but with a certain trust, that we can help Opel to accelerate its economic reconstruction,” Mr. Tavares told reporters at a news conference on Monday. “We see that there’s a similarity between the difficulties Opel is going through today and PSA’s situation three, four years ago.”
The French government would certainly balk if there were hints of further cuts by PSA in France. Amid huge protests, PSA closed a Peugeot and Citroën factory in Aulnay-sous-Bois, an economically disadvantaged suburb of Paris. The 3,000 job losses hit workers who have for the most part been unable to find work since, adding to an undercurrent of tension in the area.
The French government has already demonstrated that, at least during an election year, it will intervene to protect jobs. The Hollande administration threatened several years ago to nationalize an ailing steel plant run by ArcelorMittal to stem possible job losses, and it prevented Yahoo from taking a majority stake in a French company, Dailymotion.
When Alstom tried to shut down a train factory in the working-class city of Belfort in the autumn, Mr. Hollande, who had come under fire for France’s high unemployment rate, reacted with fury. Although the company vowed that the factory’s 400 jobs would be relocated to a larger site in northern France, the government insisted that the site remain open, and it then placed a multibillion-euro order for trains to keep the operation running.
Mr. Tavares of PSA emphasized several times on Monday that the Opel deal was not based on job cuts. “Shutting down a plant is rather simplistic,” he said. “The only thing that protects us is performance.”
But politics cannot defy economics forever. Without growth, PSA will have no choice but to cut costs.