Llodra had won their only previous meeting, five years ago in Lyon, but this time Gicquel was more clinical, converting two of his five break-point opportunities, whereas Llodra took only one of eight chances. Both players had six aces.
Gicquel next plays countryman Gilles Simon, who is seeded second.
In other first-round matches, Uzbekistan's Denis Istomin also advanced, winning 6-4, 7-5 against qualifier Marsel Ilhan of Turkey and next plays fourth-seeded Dmitry Tursunov of Russia.
Adrian Mannarino beat Vincent Millot 6-4, 6-4 in another all-French match.