I'm Lucy, and I'd be happy to answer your questions today.
The vast majority of contracts are binding without any written document at all, and therefore an email would only be proof that an oral agreement existed. An e-signature doesn't have to be used in that scenario, and there's no need for an e-sign disclosure. There are a few exceptions, set out in Fl. Stat., Section 725.01: a promise in anticipation of marriage, a promise to pay someone else's debt, a real estate sale, a contract that cannot be performed within one year, or a guarantee of a medical outcome.
Those few types of agreements require "some note or memorandum thereof shall be in writing and signed by the party to be charged therewith," but most contracts do not. An e-sign agreement helps the parties in case they have to prove that the other person signed the email, but it's not required.
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