This terrorism could lead to the break up of the EU because the EU has open borders between EU countries, but individual countries have no control over who the other countries let in.
So let's say, hypothetically, that one country in the EU - we'll call it Germany - has a very liberal immigration policy and is letting in thousands of people claiming to be refugees from areas rife with terrorists, and amongst those immigrants are likely many terrorists. And let's also say that many of the immigrants are not terrorists, but they bring with them a culture where it's fine/normal to attack, molest, rape and even kill non-Muslim women.
So, Germany's has the right to let in anyone they want. That is their choice. But if another EU country - let's call it France - does not
want to allow those people into their country, they are screwed. They are subject to the whims of the other EU countries as long as they are part of the EU, since once someone is in any EU nation, the law is that they can cross the borders into other EU nations freely.
Originally, that was one of the big selling points of the EU - ease of travel and commerce amongst nations. (Kind of like the states in the US. Once you're in the US, you're in. You can cross into any state.)
Now, with terrorism, what it means is that individual countries in the EU do not have control of their borders or sovereignty.
I believe this was a driving factor in BREXIT.