Ouanna, a wild card, defeated Nicolas Lapentti 6-3, 1-6, 6-3 for only his second ATP match win.
Also, fourth-seeded Gilles Simon, seventh-seeded Robin Soderling, and eighth-seeded Paul-Henri Mathieu won first-round matches.
After knocking out 2000 champion Arnaud Clement, Benneteau converted four of 13 break chances against Robredo.
"I knew there was a good opportunity,'' Benneteau said. "It's been a long time since I played like that. I've worked a lot on my backhand, which is my strong point. I'm also concentrating better.''
Benneteau will next face either second-seeded Richard Gasquet or Steve Darcis in his second consecutive Lyon quarterfinals. Ouanna, ranked 182nd, next meets either compatriot Simon or Andreas Seppi of Italy.
Simon, coming off the Madrid Masters final, was down a set and 4-2 before recovering to beat Juan Monaco of Argentina 2-6, 6-4, 6-1.
Sweden's Soderling beat Thierry Ascione of France 6-4, 6-1, and France's Mathieu defeated Guillermo Canas of Argentina 6-3, 6-4 at the indoor arena.
Mathieu, the 2002 champion, next meets Juan Carlos Ferrero of Spain, the 2003 French Open champion.
"Ferrero is solid. I know he's less at ease on this type of surface but you never know what to expect against him,'' Mathieu said. "I feel good here. It's the sixth time I've played, I have some great memories. I want to go all the way.''
Also, Christophe Rochus of Belgium beat Gilles Muller of Luxembourg 6-2, 6-4.
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