Loss Trial, need to pay attorney fees? If I don't what happens

What is the name of your state (only U.S. law)? FL

If the plaintiff sues a business and the company hires an attorney and loses and the defendant is granted attorney fees but the plaintiff does not pay what recourse does the defendant have?

Well, if the court ordered them (was there a contract or statue that allows it?) then the defendant has two options:
a) pay
b) appeal

If he does neither then the defendant may start proceedings to collect; the defendant does not have to but they certainly can if they desire.