I'm not sure which law governs your employment agreement, since the employer could be out of state, and your agreement could recite that it's governed by some law other than Florida's. But assuming it's Florida law (and since I'm not admitted to practice in Florida), only an attorney licensed to practice there can advise you properly. Specifically, I believe Florida limits the scope of what non-compete agreements are enforceable, based on the time of the restriction, the employer's line of business and that the restriction is reasonably necessary to protect the employer's legitimate business interests. But you would, as you suspect, be prudent not to sign the termination agreement which includes the non-compete in order to avoid being bound by it, until you consult a Florida attorney.
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