There is a lot of ways you can live in Europe. You can go by exchange programs, by campus france, by your own citizenship (if you have an european citizenship), etc. Let me explain a little better…
The first thing you have to do is to answer the question Am I an European Citizen?
You don’t have to born in Europe to be a citizen, if you’re descendant of an Italian (like I am) you can be an European Citizen, just have to prove it to them.
If you are an European Citizen, you may go to Anywhere you want in Europe, doesn’t matter if you’re french and want to go to Spain or Portugal, for example. If you want to study college in Paris, you can just apply to it online and follow the steps they say to you. Just a thing, most of them are in French, so if you don’t speak the language it may be a little difficult…But I’ll explain about Paris University later.
If you’re not an European Citizen, things may get a little harder… Depends on your way to see things! You ca just go and stay there ilegally, which I actually don’t recommend, apply to an university by Campus France, which I’ll explain later how works or apply online to find people who wants to contract people from your country to live there (they usually provide everything you may need).