in the state of florida if a defendant is found not guilty can the state file for a appeal in a murder trial
Acquittals are final in all state and federal courts. The government cannot appeal an acquittal.
Some jurisdictions recognize an exception where the defendant bribed, threatened or otherwise tampered with the judge or jury. That exception rarely comes into play. Even when it does, it would support only a new trial and not an appeal. In any other case, re-trying a defendant who has been acquitted would be double jeopardy -- which is barred by the Fifth Amendment to the United States Constitution.