once a person takes a plea deal and signs it, if they are not guilty, is there any way to have a fair trial in court
Once you plea- you are guilty!
You would have to file a motion to withdraw your plea. If the judge grants your motion, you can then go to trial.
A motion to withdraw a plea is not automatically granted just because you change your mind. Talk to your lawyer (or a new lawyer) to discuss.
If you take a plea deal you will never get to a trial. You are guilty.