You pay for Internet. So no. It is impossible.

I think people with a natural talent for languages can learn a language for free if they have sufficient inner motivation, time, self-discipline and perseverance.  However, most people lack one or more of these at varying stages of their lives.  I am only persevering with learning Italian because I have a lesson with a teacher every week, come rain or shine.  Otherwise, other commitments would have caused me to lose heart by now.  

Even language exchanges are hard to make work effectively in the long run, in my experience.  I'm not saying this just because I'm a teacher! 

I know of a few people who have learned English without any lessons or paying. I have some information and observations though. 

One guy from the Czech Republic only learned English from TV. When he came to Ireland he knew enough to get a job. This was about 8 years ago. His English improved because he was speaking English daily with me and customers. However I met him for a coffee and his English is not as good anymore because he lives with other Czech people and has been made redundant. I think if he still had to speak English he would have improved even more.

I know of people who have learned English for free using Memrise and language partners. Though it is not always easy to get partners.

May be not free but we can exchange language one others. 

I'm sorry to read from Matteo that he was mocked by some teachers for learning Spanish.  Mockery is not a legitimate tool for a language teacher, even if the student is making an obviously unwise decision in his or her learning.  If a student believes they have been mocked, it is good to raise it with the teacher as soon as possible.  There may have been a misunderstanding which can be resolved quickly, or if necessary, an apology can be made.