Hello from Sweden. Not only is primary, secondary (high school) and tertiary (college/university) education completely free, you also get paid a small amount to study if you do so full time and have no income. I got paid around $110 per month in secondary school and $370 per month in tertiary school. You get paid the same in primary school as secondary school, though your parents get the money instead of you.
You can go to any primary school you want.
You can choose any secondary school course that you have the grades for. Only the applicants with the highest grades get entry. There are almost always courses available that have no grade requirements because the course isn't full.
You can choose any tertiary school course that you have the clearance (having completed certain classes in secondary school, sometimes an additional entry test as well) and grades for. Grade requirements for entry in tertiary school work similarly to secondary school.
Secondary school is often of two types; preparation for the workforce or for tertiary education.
If you choose the former, the list of choices is very long. You can essentially find a school for any type of job that doesn't require a tertiary degree.
If you choose the latter, there are mainly three different programs; natural sciences, social studies and economy. There are more, though these three represent the vast majority of students. Each of these programs have their own choices for specialization. You could for example choose natural sciences with a specialization for social studies.
In secondary school in preparation for tertiary education you are also required to choose at least two additional classes not directly related to your program. Choosing more than four would usually result in scheduling problems. I could freely choose between ~25 different classes in a relatively small school. Choices varied from music, to politcal science to astronomy and everything in between. This contributes to your final grades. Some classes like more advanced mathematics also give you an additional boost in grades from simply passing the class and are required for some tertiary school programs.
Tertiary education structure is pretty standard. Most people choose a program and complete the courses within it. Programs are usually three or five years long. The list of programs in any major institution is pretty damn long. Many institutions have some kind of specialty, like technology or economy. There is usually enough free time to choose additional courses outside of the program, kind of like having a minor in the US, though this is not obligatory. I certainly did not see any lack of choice in tertiary education.
TL;DR: Your observation "You can't have choice and free" is objectively wrong.