Duels had introduced a form of public procedure ; the attack and the defense were equally known : “The witnesses,” says Beaumanoir, “must state their testimony openly.” 
Boutillier’s commentator says he learned from former practitioners and from some old handwritten trials that formerly criminal trials in France were held publicly, and in a form hardly different from the public judgments of the Romans.  This was tied to the ignorance of writing, common in those times. The practice of writing captures thoughts, and can establish secrecy ; but when it is not practiced, only publicity of the procedure can fix those same thoughts.
And as there could be uncertainty about what had been judged by men or pleaded before men,  the memory of it could be recalled whenever court was held by what was called procedure by attestation  ; and in this case challenging witnesses to combat was not allowed, for cases would never have seen their end.
Subsequently, a new form of hidden procedure was introduced. Everything was public ; everything became hidden : interrogations, inquiries, verification, confrontation, the conclusions of the public prosecutor  : and that is the practice today. The first form of proceeding suited the government then, as the new one was appropriate to the government established since.
Boutillier’s commentator dates this change to the ordinance of 1539. I think it occurred little by little, and that it passed from one seigniory to the next, as lords were giving up the old practice of judging, and the one taken from the Establishments of St. Louis was progressively improved. Indeed Beaumanoir says that it was only in the cases where gages of battle could be proffered that witnesses were heard publicly ; in the others, they were heard privately, and their depositions were written down.  Thus procedures became private when there were no more gauges of battle.