To start, the EU wants to "fully deploy" 5G mobile networks across its member countries by 2025. You'd theoretically get gigabit-class data across the continent. And you might not have to be picky about using it when traveling, either. While the EU has had to shelve its most recent free roaming plan, it still wants to "abolish" roaming charges. You should see a refined take on its plan next week.
However, you might not even have to depend on cellular data to get online. The proposal would also offer free wireless internet access (presumably, over WiFi) in the "main centers of public life" of every EU town by 2020. You wouldn't get blanket coverage, but this would be particularly crucial in rural areas where cellular networks are spotty or non-existent, and local organizations don't always have the means to offer free WiFi hotspots. If a €120 million ($135 million) grant receives approval, communities would have access to the funds before the end of 2017.
The EU is committed to its promises of erasing borders for media services, too. It wants to make content accessible across the Union, so you wouldn't be limited to material offered in your home country. You could watch German Netflix shows while you're visiting France, for example. You could also buy pay-TV movies and similar material from other countries, some of which might well be less expensive than it is at home. Broadcasters would still have control over whether or not their content is available in other countries.
It's in the copyright space where things get tricky. The proposal would require better data sharing and transparency for creators, but it would also give press publishers rights that ensure they get a "fair share" of revenues for material they post online. Sound familiar? It should -- it's similar to laws in Germany and Spain that ask search engines like Google to pay up when they show an article snippet in their results. The EU contends that this is necessary to make sure writers are "paid fairly," but Google unsurprisingly objects. It believes that the German and Spanish laws "failed," and that these demands for payment ultimately hurt publishers by giving web users fewer reasons to click through to an article.
Moreover, the regulation might be bad news for YouTube. The proposal would require that services offering user-uploaded content take "appropriate and proportionate" steps to protect copyright. While this does include "content recognition technologies" (possibly a reference to YouTube's Content ID), Google is worried that the measure would require screening content before it goes public, which would demand far more work. Google policy lead Caroline Atkinson claims that it would lead to an internet where every upload would have to be "cleared by lawyers."
The proposal needs to clear both the European Parliament and individual governments to go forward. It may take a long time before the initiative takes effect, and that's assuming there are no significant changes. If it does, though, Europe could have a very different digital landscape within the next decade. It would definitely be more connected, but there's a concern that Google and others like it might scale back their European presence rather than make the effort to comply with new copyright laws.