Why the focus on IT? Automobiles, trains, embedded controllers, space and commercial flight, weapon systems, high-tech manufacturing. All those are areas where Europe has at least one industry leader.
There are so many companies you never hear about because you aren't in the industry they operate in.
Because the question was about outcompeting. Automobiles, etc., there are many competitors, including some American. And weapon systems, there is a national security reason to maintain regional leaders, no matter how inefficient.
In IT, I find it funny that Google has a higher market share in Europe than in the US.
Why outcompete? Why the need for a quasi-monopoly? Why can't half a dozen companies work a market in competition and create better products for everyone? Many problems with Facebook and Google come from not it outcompeting other companies and making things worse for society as a whole.
There are so many companies you never hear about because you aren't in the industry they operate in.