French police searched the Paris headquarters of U.S. fast-food giant McDonald’s on May 18 on suspicion of aggravated tax fraud. (Kenzo Tribouillard/AFP/Getty Images)

French authorities recently raided the Paris headquarters of two U.S. corporate giants, Google and McDonald’s. The European Commission is investigating tax deals that Amazon and Apple reached in Luxembourg and Ireland. And the commission has also accused the Netherlands of allowing Starbucks to avoid more than $30 million in taxes.

Across Europe, just how much — or little — U.S. multi­­national firms are paying in taxes is coming under intense scrutiny.

While the U.S. companies say they are paying what they owe, European authorities have argued that many firms have developed complex tax strategies to lower their tax bills, sometimes with the help of countries hungry for the jobs they can bring.

The battle playing out across Europe mimics, in many ways, a debate that has sparked populist anger in the United States: Are U.S. companies getting special treatment, or are they being unfairly targeted?

The fight, in essence, centers on the more than $2 trillion in overseas profits that U.S. corporations have refused to bring back to the United States, where they would face a hefty tax bill. U.S. lawmakers and regulators have lamented the practice but have had little success in pressing the corporations to bring the money home.

Now European tax authorities are also eyeing this money, international tax experts say. The profits have often been routed through low-tax European countries, potentially cheating others nations in which the companies operate, they argue.

“The Americans, we haven’t been doing anything about this. In the meantime, the Europeans, facing serious austerity, they look at this [money] and say, ‘Some of it belongs to us,’ ” said Reuven S. Avi-Yonah, a University of Michigan law professor who specializes in corporate and international taxation.

“It looks to me that they are going to tax it first,” he said. “What worries me is that we will lose the opportunity to collect some of that income, especially on the stuff that has been earned already.”

If Europe is successful in increasing the amount U.S. companies pay in overseas taxes, that would lower the amount that could be collected in the United States, international tax experts say.

Many U.S. multi­national corporations have established European headquarters in low-tax countries. Apple runs its European operations from Ireland, which has a 12.5 percent corporate tax rate. In 2005, Amazon set up its European operations in Luxembourg, which is known for striking generous tax arrangements. ( founder Jeffrey P. Bezos owns The Washington Post.)

But with public spending in many European countries restrained after the financial crisis of 2008 and amid a growing global debate over wealth inequality, the practice is getting increasing scrutiny. (Most of the investigations revolve around the issue of “transfer pricing,” when one part of a large company sells goods or services to another part of the company.)

Late last year, Apple agreed to pay $350 million in back taxes to Italy to settle a dispute there, but some estimate the tech giant could owe the Irish government $8 billion to $19 billion for underpaid taxes depending on the outcome of a European Commission investigation.

Apple, which says it paid $13 billion in taxes last year, pointed to a 2014 statement in which it previously said it had not received special treatment from Ireland.

“Through our investments in jobs and innovation and our contributions to economic growth in global markets, Apple has become what we believe is the largest taxpayer in the world. We pay taxes wherever we operate in accordance with the law,” Cathy Kearney, Apple’s vice president of European operations, told the European Parliament in March.

McDonald’s, which has nearly 8,000 restaurants in Europe, has acknowledged that French authorities searched its Paris headquarters on May 18. In a statement, the company said it complies with all tax laws, including payments of tax owed in each country in which it operates. The European Commission is also investigating the company’s tax deals in Luxembourg.

“A tax ruling that agrees to McDonald’s paying no tax on their European royalties either in Luxembourg or in the US has to be looked at very carefully under EU state aid rules,” Margrethe Vestager, in charge of the commission’s competition policy, said in a statement. “The purpose of Double Taxation treaties between countries is to avoid double taxation — not to justify double non-taxation.”

Google has also become a flash point in the debate. The search giant, which is owned by the holding company Alphabet, has its European headquarters in Ireland.

In January, Google agreed to pay $185 million in back taxes to Britain. But the settlement has many critics, who say the company should have paid much more.

And it hasn’t stopped other countries from coming after Google for back taxes.

Last week, French police raided Google’s French headquarters, looking for evidence of “aggravated tax fraud and organized money laundering,” France’s financial prosecutor’s office said in its statement, according to the Associated Press.

At the center of the debate is the way in which the company counts profits eligible to be taxed in France, where the corporate tax rate is more than 30 percent. France is arguing that Google does more than it claims in the country, signing contracts rather than just advertising and research.

“We comply with the tax law in France, as in every other country in which we operate. We are cooperating fully with the authorities in Paris to answer their questions, as always,” a Google spokesman said in a statement.

Europe’s strong response has angered the Obama administration, which worries U.S. firms are being targeted for unfair treatment that could ultimately hurt American taxpayers.

These cases appear to “be targeting U.S. companies disproportionately. The legal theory underlying its investigations logically should apply to all multi­national firms, not just those based in the United States,” Treasury Secretary Jack Lew wrote to Jean-Claude Juncker, president of the European Commission, in a February letter.

A bipartisan group of senators — Orrin G. Hatch (R-Utah), head of the Senate Finance Committee, Ron Wyden (D-Ore.), Rob Portman (R-Ohio) and Charles E. Schumer (D-N.Y.) — have also weighed in on behalf of the U.S. multi­nationals.

“We are disappointed that, to date, [European Commission] officials generally have dismissed our concerns and continue to insist they are not targeting U.S. companies,” the senators wrote in a letter to Lew earlier this week. “At the same time, their responses have actually shown our concerns are justified.”