I expect you will see barriers come up over time that make it more difficult for American tech companies in Europe. It makes no sense for the EU to outsource such a valuable part of the economy.
Again, protectionism is a dangerous road. If the EU blocked American tech companies, the US would retaliate in kind. While it's possible that Europe could eventually become self-sustaining if given a friendly environment to grow indigenous tech companies, losing access to every major OS overnight (as just a small example of the potential retaliation) would be a pretty devastating experience for Europe. You can't replace Microsoft, Apple, and Google overnight.
