BRUSSELS—When Adrian Johnson saw a request for volunteers to speak at his children’s career fair, the high-tech entrepreneur jumped at the chance to explain his profession. But the school in Fontainebleau, France, turned him down.

“They wanted doctors or people who worked at BNP Paribas,” said Mr. Johnson, a Briton who has started Web companies in France, Germany and the U.K. “The idea of having a weird guy who started companies—they didn’t want their kids to hear that.”

As Internet firms push farther into the terrain of mainstream industries, from publishing to telecoms, policy makers in Europe are increasingly concerned about the lack of home-grown rivals to compete against dominant U.S. players like Google Inc. and Facebook Inc. Their solution: knit the region’s 28 national ecosystems together into a vast digital market that could become a breeding ground for the Web giants of the future.

But these grand plans may not be enough to overcome a European culture that has long been unfriendly to entrepreneurs, valuing prudence, professionalism and leisure time over flamboyant risk-taking.

That culture is a particular liability when it comes to the increasingly crucial high-tech field, whose culture and lore are wrapped up in startups, from Steve Jobs in his garage to Mark Zuckerberg in his dorm room.