Parra moves from scrum-half to replace Francois Trinh-Duc after producing a fine kicking display in the 46-19 victory over Canada on Sunday.
The Clermont back becomes the second player in the history of the World Cup to start matches at nine and 10. Saturday will also be his first start for France in the position.
In total there are five changes in personnel and two positional switches to the XV that thumped Canada.
Dimitri Yachvili is named at scrum-half, David Marty drops out of the XV so Aurelien Rougerie is restored at outside centre with Maxime Medard picked on the wing.
Dimitri Szarzewski makes his first appearance in New Zealand at hooker in place of William Servat, while lock Lionel Nallet and flanker Thierry Dusautoir come in for Romain Millo-Chluski and Fulgence Ouedraogo.
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