You would have to contact FSU directly. The acceptance of credits is solely up to the individual colleges. However, PFHS is nationally and regionally accredited. So call or go directly into the admissions office and ask if they will accept it. Be sure that you tell them that the school is regionally accredited by the middle states and specifically mention PF by name. If you just say "online high school," you might not get the right response.
That said, I can tell you that Miami Dade and Broward College do accept it. In terms of FSU, be aware that since this is a flagship university, they are very competitive and require high SAT/ACT scores and high GPA. It helps if you take some advanced courses. Florida curriculum requires students to have at least Algebra 1, so make sure you take that here. Not being accepted there may have nothing to do with the fact that you're attending PF but of the competitive nature of that particular school.
That said, here is a little advice. Florida has the 2+2 program, which means that if you attend a community college in Florida, you are automatically accepted into ANY state university, including FSU and UF.
I would say that Florida is more open to online high schools since they have their own public online high school.