What's the name of this Caffe Tube for students?

Sers, since I'm not so easy to learn at home, I'm looking for a kind of cafeshop as you know something on the movies, where the students sit around with their laptop and learn, you can suggest such places here in Frankfurt?

That's what Café is called. Of course, not every café in Germany looks like a US teen movie, but one of its equivalent is Starbucks and others.

We used to go to the library of the department earlier…

Unlike in the movie, the operators will find it less good if you because 4 hours long block a table and only order a coffee

The term used today is "cowork space" or "coworking". We speak less and less German. However, they usually cost money. Otherwise you can sit in any normal café. Most offer Wi-Fi.

https://coworkingguide.de/coworking-frankfurt/

A library would be just as suitable.

That's right, thanks.