Williams could meet Jelena Jankovic in round three

Cornet, 17, put up a spirited challenge and would have served for the first set had she converted a break point at 4-4.

Williams was inconsistent and dropped serve three times but she eventually came through 6-4 6-3.

The match was one of only six to be completed in the women's draw as rain played havoc with the schedule again.

French Open tennis: Victory for Venus

Williams and Cornet had just finished their warm-up at 1000 BST when a heavy shower forced the players off.

They eventually returned at just gone 1300 BST and Williams took one hour and 28 minutes to reach the second round before the wet weather returned.

606: DEBATE Your views on Williams' victory

Williams is playing in her first Grand Slam of the season after missing the Australian Open with a wrist injury but she believes she is a threat to the title contenders.

"The most important thing is I'm on tour, then things can happen," she said. "I am just happy to be back out there and fit.

"But I'm a winner. I am counting my blessings but I definitely expect things from myself."

Elsewhere on Monday, Michaella Krajicek posted a 6-3 6-3 win over 31st seed Severine Bremond - who became the first seed to be eliminated from the tournament.

China's 16th seed Li Na beat Germany's Sandra Kloesel 7-6 (7-4) 6-0 while Australian Samantha Stosur thrashed American Jamea Jackson 6-1 6-2.