In Florida, does divorce decree have to be signed and dated by both parties to be final?

In Florida neither of the parties has to sign a final judgment, just the judge signs it. The judge will not enter a final judgment unless all other necessary documents have been signed by the parties, and it depends upon the judge as to whether a divorce can be granted pursuant to a motion for judgment on the pleadings.

The Final Judgment is only signed by the Judge, not the parties.

Agreements have to be signed by both parties to the case. The actual Order is signed by the court.

You don't say what "papers" were sent to you for signature, or who sent them, however, generally speaking, in the absence of a fully-signed Marital Settlement Agreement, your case would have to be set for a trial, rather than an uncontested final hearing. If set for trial, and you both do not intend to proceed with the divorce, you should prepare and file a motion for continuance, and schedule that motion for a hearing before the court. If set for an uncontested final hearing, and you both do not intend to proceed, you should file a notice of cancellation of hearing with the court.