There is no common law marriage in FL -- in TX, there is, but not in FL. But FL judges permit adultery by a spouse in a "loving" relationship.
After the Court's ruling in Lawrence v. Texas, I don't think any adultery law which provides a criminal penalty can be enforced.
Presumably it can still be statutory grounds for a divorce, but I'm not sure how many states haven't essentially adopted a "no-fault" divorce law anyway.