Gicquel, the runner-up in an all-French Lyon final in 2006, ousted Robredo 6-4, 7-6 (7-5) in one of the first matches of the indoor tournament, which runs through Sunday.
Mardy Fish also knocked out a seeded player, stopping No. 7 Nicolas Almagro 2-6, 6-3, 7-6 (7-4).
Andy Roddick is the No. 1 seed for the tournament and is trying to win back the title he claimed in 2005,