BRUSSELS—The European Union on Tuesday called on U.S. President Joe Biden to help draw up a common rule book to rein in the power of big tech companies like Facebook and Twitter and combat the spread of fake news that is eating away at Western democracies. In a speech to the Davos World Economic Forum, European Commission President Ursula von der Leyen urged the Biden administration to join forces against “the darker sides of the digital world,” which she said was partly behind the “shock” storming of Capitol Hill on Jan. 6. “The business model of online platforms has an impact and not only on free and fair competition, but also on our democracies, our security, and on the quality of our information,” von der Leyen said. “That is why we need to contain this immense power of the big digital companies.” The head of the EU’s executive body called …