Would I have a case in the following situation?
I was fired exactly 1 month ago because a register was found $200 short. I was the last person to touch the register since I was helping an associate with a transaction. The money didn't add up, but I knew I didn't take anything. Today I found out that three other associates were fired, and it was because they were the ones who had actually stolen the money.
There is documentation of the reasons for my firing and their firings, and I'm sure it can be used as evidence during trial.
I agree with Ms. Slack's answer, and wanted to add that, in my opinion, you would still qualify for unemployment compensation.
Additionally, if the information you posted is accurate, your ex-employer should not be able to give you a bad reference if a prospective employer were to call and ask about you.
As an at-will employee, which all employees are in Florida absent a written contract for a specific term or a union, an employer can fire you for no reason, a good or bad reason, fair or unfair reason, correct or incorrect reason, etc..
Your primary, though not exclusive protection, is from discrimination on the basis of gender, race, religion, age, national origin, disability, or pregnancy. You have other rights if you are a whistleblower, are fired for jury service, for taking FMLA leave, etc.
However, absent something other than being fired for a reason where the employer was wrong about the facts it would not appear you have a claim for wrongful termination. You would, however, have the right to unemployment. That said, it could be challenged for misconduct given the facts you provided, and a hearing officer would need to end up believing that the employer has not proven misconduct sufficient to deny unemployment.
Florida is an employment at-will state and your employer can fire you for any reason or no reason, with or without cause, so long as you do not have a written contract for employment or the termination is not for a prohibited reason (such as discrimination under Title VII).
Thus, your employer didn't need a reason to fire you; whether you stole the money or not. Florida also provides a qualified immunity to previous employers who provide job references to prospective employers. It is difficult to overcome the qualified immunity.
Why do you think your employer really terminated you?
Assuming you are an at-will employee (without an employment contract or union membership), your employer can terminate you at any time for almost any reason. If your employer terminated you because he thought you stole money, his actions were not illegal. This is true even if his assumption was wrong. And even if he later realized he was wrong and refused to rehire you.