For decades, France’s Valdunes SAS charged premium prices for the wheels it made for high-speed trains and other rail systems around the world. That strategy changed after a Chinese state-owned industrial conglomerate bought the company in 2014. The new owner, Maanshan Iron & Steel Co., or MA Steel, slashed prices in a bid to dominate the market. “We were told that we shouldn’t miss a single order. That was explicit,” recalled Jérôme Duchange, Valdunes’s former top executive in France. “They have an appetite for economic conquest.”

The French firm was now in the service of the steel company’s larger strategic goals—to give it the know-how to make wheels for high-speed trains in Chinese factories, and to gain access to Europe’s highly regulated rail sector and other markets world-wide. For that, Valdunes received low-cost credit from Chinese government banks and 150 million euros, equivalent to $181 million, from MA Steel to stay afloat.

Over the past decade, China has provided billions of dollars of subsidies to state-owned companies to acquire Western manufacturing rivals and to build factories beyond its own borders. Now, these overseas factories are roiling global markets with low-price goods in sectors ranging from automotive tires and rail equipment to fiberglass and steel.

“Chinese companies are expanding. They are investing everywhere,” said Luisa Santos, deputy director of BusinessEurope, the region’s main business association. “This means that the flaws we see in the Chinese market are now being exported to other markets.”

The European Union this week proposed legislation to rein in companies in Europe that are subsidized by foreign governments, one of a series of measures that aim to counter the global expansion of Chinese firms.

Zhang Ming, the Chinese ambassador to the 27-nation bloc, has said Europe’s stance has worried Chinese investors in the region and undermined the EU’s historical openness to foreign investment. “We often see the EU as our professor for building our market economy,” Mr. Zhang said. “So we don’t want to see our professor and our partner have any hesitation when it comes to these principles.”

Daniel Gros, an economist at the Centre for European Policy Studies, a think tank in Brussels, said those differences shouldn’t lead the EU to penalize China for investing abroad. “Sorry, we cannot export our own model,” he said. “And we have lots of other subsidies. The footprint of our governments in our economies is very, very large.”

The U.S. and Europe have long relied on the World Trade Organization and tariffs to penalize China for subsidizing exports with grants, tax breaks and credit from state-owned banks, measures that helped the country grow rapidly. But the WTO rules weren’t written to constrain subsidies that a government gives to its manufacturers overseas.

The result: Chinese-owned factories outside of China usually face lower tariffs than those imposed on factories inside the country—or escape them altogether.

Western officials and executives say financial support from the Chinese government allows Chinese-owned manufacturers overseas to operate on razor-thin margins or at a loss, while they grab market share or serve the strategic objectives of the government. The problem, they say, is particularly difficult to address when the manufacturer in question is operating inside a Western market.