Dupont did not have a trial because the only legal framework for it under the constitution would have been an Imperial High Court (I forget the exact name) which had never been set up. The Commission that judged him was appointed to investigate and advise by Napoleon.
I don't know whether the French Constitution required trials to be held in public but since the public were admitted (under police supervision) to Moreau's trial it would seem that it was normal procedure. The maxim of English law is "Justice must not only be done but be seen to be done".
I know there was widespread corruption in the British system (no-one has denied it) but there was a mechanism, however clumsy, for it to be investigated and publicised. That was what was lacking in the French system.