The 13-year-old girl, who has not been officially named, originally told her father that Paty had asked Muslim students to leave the classroom while he showed the cartoon during a class on free speech and blasphemy.
According to evidence given by the girl seen by French media she said: "I didn't see the cartoons, it was a girl in my class who showed me them."
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The girl's father filed a legal complaint against the teacher and began a social media campaign over the incident based on his daughter's account. He identified Paty and the school in Conflans-Sainte-Honorine, west of Paris.
Prosecutors said shortly after the killing that there was a "direct causal link" between the online incitement against Paty and his murder.
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It then emerged that the campaign against the history and geography teacher had been based on a distorted account of what had happened in class days earlier.
As he had done in similar lessons on free speech in previous years, Paty warned students that he was about to show a depiction of Muhammad. He said anyone who thought they might be offended could close their eyes.
The girl had originally claimed the teacher had asked Muslim pupils to leave the room. When she objected she was suspended from school, she said. It now appears that the girl was suspended the day before the class was given, according to Le Parisien newspaper, because of repeated absence from school.
The girl explains in her leaked testimony that she made up the story so as not to disappoint her father.