This is an interesting question and more facts would be needed regarding how that relationship started and what were its terms.
As a general rule, assuming the employee was not a member of a labor union, not a government employee, and subject to an enforceable employment contract, the employee can be terminated for any reason not prohibited by law.
Here, the termination is not based on the employee's membership in any protected class, such as their race, religion, gender, etc., but is rather was a matter of convenience to the employer because the employer is embarrassed by being caught having an affair. While the employer's ethics are certainly in question, generally speaking he or she has not broken a law for firing an employee basically because his or her spouse does not like the employee (for no legally prohibited reason).
However, an employer (who has at least 15 employees) is not allowed to sexually harass an employee. If this relationship was consensual, it would normally not be actionable. But the relationship seems to have had an additional term - that term being that employer and employee will have a consensual relationship unless and until anyone finds out, at which time the employee will be terminated. That is getting dangerously close to quid pro quo sexual harassment, because it is linking the circumstances and conditions of a sexual relationship to a term of continued employment.
I certainly think the employee should consult with an employment attorney and research this issue further.
Also, I am assuming the relationship was consensual. If it was not, and if it was rather pressured, coerced or bargained for, then quid pro quo sexual harassment should apply.
This response is merely a general discussion of an issue based on the information provided. It is not intended as legal advice and does not form an attorney-client relationship. You are encouraged to seek out an attorney of your choosing in your local jurisdiction, and to discuss your legal issue with that attorney.
I agree with Mr. Callison that you should see a lawyer who represents employees for discrimination and harassment since the facts are not totally clear as to all of the circumstances. Although Florida is considered an at-will employment State where employers can fire an employee without a reason, there are over 30 exceptions to the law and there is no substitute for seeing a good lawyer in person.