The defending champion ousted Germany's Barbara Rittner, 6-2, 6-1, in opening round action on Monday at Roland Garros.
Up next for Williams will be either Indonesian Angelique Widjaja or Swiss Marie-Gaiane Mikaelian.
Williams and older sister Venus are in opposite halves of the French Open draw, which means they could meet in yet another Grand Slam final. Williams and the third-seeded Venus also met in the French Open final last year.
Serena Williams had no trouble in her first match of the 2003 French Open. (CP Photo)
Serena Williams is the reigning French Open, Wimbledon, U.S. Open and Australian Open champion. Venus finished as the runner-up all four times.
"I think players generally believe that I'm the player to beat in any tournament, especially the Slams, because I like to kick it up to a new level," said Williams after her match.
"This is what I play tennis for mostly -- to be remembered."
Other winners in women's play included No. 4 Justine Henin-Hardenne and No. 5 Amelie Mauresmo. Henin-Hardenne beat Patricia Wartusch 6-3, 7-5, and Mauresmo swept fellow Frenchwoman Virginie Razzano 6-3 7-5.
Mary Pierce, the 2000 champion, lost to Clarisa Fernandez 6-2, 6-3.
On the men's side there have been two upsets.
Fifth seed Roger Federer was stunned by unheralded Peruvian Luis Horna, 7-6 (8-6), 6-2, 7-6 (7-3). Federer committed a lofty 86 unforced errors in the shocking setback.
It marks the second time in two years that the talented Federer was an opening-round loser at Roland Garros.
The world's No. 5 Federer headed to Paris as one of the hottest players on the men's tour. He leads the circuit in match wins this season (38-9) and is second only to Andre Agassi with his three tournament titles. The Australian Open champion Agassi owns four championships.
Federer is also second only to Agassi in the all-important Champions Race.
Agassi also advanced on Monday, defeating Karol Beck 6-2, 6-3, 6-3.
"I'm here because I believe I can win," said Agassi, at 33 the oldest player in the men's draw. "I've still got a chance."
Also falling was two-time French Open runner-up Alex Corretja, the 16th seed.
with files from Sports Network
