The first experiment was that I ran a packet sniffer on my own computer and let it run for an hour. With web browsing, e-mail and chat going on I barely ran up a megabyte before compression. If two people download the same web page, then the archive only needs to store that page once along with the fact that it was seen by two people. If five people are conversing in a chat room, only one conversation needs to be stored - not five. I am not altogether convinced that the EU will pull off a project of this scale, but I don't think that it's impossible , either.
Governments do have government-scale resources, after all.
If they can launch space programs, build interstate highways, and dig channel tunnels, then they might be up to the task of implementing another enormous engineering project. They couldn't help but improve the state of mass storage and retrieval technology. I don't think you should worry about that. But I can tell you, even that logical information becomes absolutely ridiculously huge. Frankly, I personally hope they store it in triplicate.