In the round of eight, the 22-year-old will face another American, either sixth seed Mardy Fish or Robby Ginepri.
Last year, Roddick reached the quarter-finals of this dual event here - women are competing in a concurrent WTA Tour event - before falling to Sweden's Thomas Enqvist.
The other three men's matches of the day were all first-round encounters. Second seed Tommy Haas of Germany got safely through with a 6-4, 6-4 victory over American qualifier Jeff Salzenstein.
But seventh-seeded Jurgen Melzer of Austria was upset by Wayne Arthurs of Australia 7-6 (7/5), 7-6 (7/4).
Joachim Johansson of Sweden won the men's tournament last year but is not defending his title after capturing the Open 13 event in Marseille on Sunday. He is playing this week in Rotterdam.
On the women's side, top seed and defending champion Vera Zvonareva of Russia defeated Severine Beltrame of France 7-6 (7/0), 6-3 to reach the quarter-finals.
COLLATED RESULTS: (x denotes seed):
MEN (FIRST ROUND): Cyril Saulnier (FRA) bt Robert Kendrick (USA) 5-7, 6-3, 6-4; Wayne Arthurs (AUS) bt Jurgen Melzer (AUT x7) 7-6 (7/5), 7-6 (7/4); Tommy Haas (GER x2) bt Jeff Salzenstein (USA) 6-4, 6-4
(SECOND ROUND): Andy Roddick (USA x1) bt Arnaud Clement (FRA) 6-3, 6-3.
WOMEN (SECOND ROUND): Cho Yoon Jeong (KOR) bt Abigil Spears (USA) 6-4, 6-4; Akiko Morigami (JPN) bt Michaella Krajicek (NED) 6-7 (2/7), 7-6 (9/7), 6-4; Vera Zvonareva (RUS x1) bt Severine Beltrame (FRA) 7-6 (7/0), 6-3; Meghan Shaughnessy (USA x3) bt Hana Sromova (CZE) 6-3, 6-2; Nicole Vaidisova (CZE x7) bt Kristina Brandi (PUR) 6-2, 6-2; Evgenia Linetskaya (RUS x8) bt Yuka Yoshida (JPN) 6-2, 6-2; Katerina Bondarenko (UKR) bt Angela Haynes 7-6 (7/3), 7-5.