In 2010, Floyd ran unopposed for re-election to the Tennessee House of Representatives District 27.
You could wallpaper his office with petitions and he would not resign. There is nothing the Governor can or will do. There is nothing the State House of Representatives can or will do. There is nothing any court of law can or will do.
You would do better to try and contest the seat next time around, and perhaps make him spend a little money to defend his seat. Beyond that, all your indignation and $4 will buy you a cup of coffee at Starbucks. Petitions are worthless.