In an at will employment state such as Florida, an employer is allowed to condition continued employment on signing specific agreements (although this is most commonly encountered in the context of a "noncompete" agreement). One way of describing "at will" employment is that you can be terminated for any reason except for a discriminatory and/or retaliatory reason.
Note, however, that the mere facts that you sign an agreement does not necessarily make it enforceable. The law does prevent enforcement of contracts to the extent that enforcement violates public policy. It appears that you may actually need to consult with an intellectual property attorney in order to determine whether the contract itself is binding.