"That's not a phrase one associates with the EU."
No, but it's immaterial. Our own security agencies are in bed with the NSA, so there's no data independence even if they erect the great Firewall of Europe (and even in the unlikely event that it worked). But there's a bigger problem, that in terms of technological independence the US has such a lead on the core technologies, operating systems, application and web services, and indeed voluntarily surrendered data that there's nothing really to protect in Europe.
The EU and the US are similarly sized economic blocs. But the US is home to 80% of global technology by revenues of domiciled companies. Yes, there's a few diamonds in the EU clay, such as ARM, the origins of Linux, SAP (arguably), and so on. But the maths is simple, that the revenues EU tech firms are less than 10% of global tech sector revenues, and EU ownership of IP is particularly limited - all the leading web applications are US invented and controlled, there's no surviving and successful phone European commercial phone OS IP, no computer operating system commercial IP of any significance. The demise of Nokia was a purely private sector (and Finnish) disaster, but what might the EU have done to stop that? Protectionism breeds weak firms that don't survive in the market, and all of this EU prattle smells of a return to commercial nationalism and picking winners. We've tried this before with ICL (and in France with Groupe Bull), and it didn't work last time, it won;t work this time.
The best thing the EU could do would be to reduce its own regulations, and to require member countries to reduce their native regulations, but that's not going to happen. It's far too important to the bureaucrats that they can force companies to fill in their crappy forms like ESOS, make the companies responsible for providing employee pensions (ie transfer of the welfare state to companies), require them to sign up to "Climate Change Agreements", regulate the packaging they use, check the work status of their employees (because that's far too difficult for the UK Border Farce), etc etc.
You'd have to be mad to set up a new business in Europe.