YES it is FREE.

 You won't pay fees for doctoral study in Finland, regardless of your nationality.

You could even paid to earn a doctorate degree.

In Finland, the salary of an employee (PhD, Postdoc, Researcher or a Professor) has consisted of a job requirement component and a personal performance component. A PhD student is placed on Level 2 to Level 4 based on the progress of the thesis. In that case, the monthly gross salary of a PhD student is from 1970€ to 2460€.