I'm working on a screenplay loosely based around Joan of Arc, and I've come to a point in the film where a husband kills his wife with an axe and confesses to the crime, seeking forgiveness. Who would be in charge of prosecuting him? What would his typical punishment be? I'm trying to keep some sense of historical accuracy.
There is no 'typical' 'French Medieval Justice System', there was barely a 'France' for much of the medieval period: it was highly fragmented with overlapping laws (such as were written down), customs, social groups and geo-political jurisdictions. Only in the 13th century was there sufficient centralization of authority in France to begin the task of taking orally-transmitted, regional customs and turn them into codified laws. This was a process which took centuries, and did not start as a function of 'making law visible and structured' so much as the development of technique of authority. Only by 16th c was there really a structured 'law' which was represented through a system of authority recognizable to us.
This transcription of customary into 'law' was not a matter of taking down a verbal law and making it written. The process was even at times a literary one which would be foreign to us, gathering together narrative and rules in exempla. It stretched far:
beyond the purely legal-technical sphere. Very much like the popular preachers of the time, Philippe de Beaumanoir could tell the horrifying story of a pilgrim who innocently fell into the wrong company and was executed together with his casual drinking companions, and Jacques d'Ableiges could cap it with a salacious tale of a priest who lost the privilege of high justice by farting in the royal sargeant's face. [p14]
Dive into this book to find something to help your story out:
The trial of Jeanne d'Arc stands out because it was a heresy trial, and such trials were governed by canon law of the Church, a juridical system entirely separate from civil law and had developed in the Church far 'in advance' of late medieval secular criminal justice.
You might want to read some case examples in Medieval Justice: Cases and Laws in France, England and Germany, 500-1500 by Hunt Janin. There's an entire chapter focusing on case samples and they should give you a good solid idea of how to proceed with your screenplay.