project itself between two groups that want to kill each other and think they will be successful there.

Because Israel wouldn't attack them and the other group won't have many weapons left when the IDF is finished with them. Obviously it won't be the EU alone as it would be seen as too one sided (well Ireland maybe not), but let's not forget that we're talking about a 360km² area with less than 2 million people here. This isn't a huge landlocked mountain country like Afghanistan, it's a tiny strip of desert with a modern harbor in walking distance. For reference you can look at the manpower KFOR and similar missions have.

It's not going to be easy to get political approval but a UN mission would almost certainly be able to keep the peace there.