The share of EU companies among the largest in the world has been declining: "In 2000 nearly a third of the combined value of the world’s 1,000 biggest listed firms was in Europe, and a quarter of their profits. In just 20 years those figures have fallen by almost half."
Here's the EU share of the global economy, and also the stock market capitalization of EU companies compared to global stock market capitalization. The message here is not just that both shares have declined substantially. Notice also that back around 2000 the EU share of the global economy and the share of the EU in global stock market capitalization were roughly the same, but that is no longer true.
Europe has often been a world leader in drawing up rules and regulations that companies must follow, in areas including digital privacy, environmental protection, use of genetic modification technologies, and so on. However, the EU countries have overall, judging by performance, have not been an especially friendly place to start or run a company, The European Union itself remains a fractured economic zone, separated by barriers set up by national governments, as well as by language and cultural differences.
The Economist writes that big EU companies have in recent decades been preferring to expand their sales and operations overseas, rather than in their home base.
Companies are social mechanisms both for organizing current and future production, and also for planning and investment needed for future innovations in production methods and new products. Europe has a smaller share of these engines of production.