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French criminal courts have had to rule on the guilt of Rwandans for their involvement in the genocide of Tutsi in Rwanda twenty years earlier. French criminal justice has thus become one of the links in a global justice system capable of trying all perpetrators of crimes against humanity, anywhere. The academic literature on these subjects enshrines the advent of unified justice in its categories, actors and practices, and placed at the service of a common cause: neo-imperialism or the human rights of victims. This article, based on the observation of several of these trials, shows on the contrary these trials consist of local frictions and misunderstandings, which guide the probative demonstration. While these trials—links in a chain of scenes of justice around the world—impose particular roles on witnesses, it is the local procedures that determine what can be said about genocide.