Having a common (second) language is a first step towards understanding each other's culture better. And that in turn facilitates a federal EU. It can't be done overnight, but it is a goal I wish we would pursue more actively.
Each culture's language is an integral part of their culture, and their culture wouldn't be the same if they switched to speaking another another culture's language.
One or two years at school would be enough, which means that the entire problem could be fixed in a year.
But that's not how things work in real life. Just because something is a good idea doesn't mean it's going to happen.
The idea that a language, any language, can be learned in a year or two is not consistent with observation. Just think of any immigrant you have ever ran into in real life.