What should a student do when they are the victim of a FERPA violation? A student was subject to a clear  Family Educational Rights and Privacy Act (FERPA) violation by a professor. 
Does student have any rights against the professor? 
How should they proceed when they are the victim of a FERPA violation?
In the US, you have the right to file a FERPA complaint. The instructions are posted on the Government website.  If the Government decides that there was a FERPA violation, there are two possible outcomes:


They agree that the university will bring itself into compliance, or
They do not agree that the university will bring itself into compliance, and therefore, the university will lose their eligibility for federal funding. 


The latter of these is an existential threat to the university; therefore, the first one is almost certain to happen. However, the university could discipline the professor as a way to demonstrate that they take being in compliance seriously.

Beyond this, I think the key question for you is what is your goal? 


Students do not have the right to sue over FERPA violations, so  a financial or other settlement for the student is highly unlikely. 
If you want some specific action (e.g., being allowed to complete your degree without interacting with this professor), you should request this through the usual channels (start with the department chair, then the dean). You could mention that you believe this is a FERPA violation, but I would avoid making threats.    
If you're just angry and want "justice," you could also complain to a dean, department chair, or even ombudsman, or could submit the FERPA complaint. It's hard for students to prevail against professors, however, particularly if this is the first complaint.