World number one Caroline Wozniacki crushed Japan's Kimiko Date-Krumm 6-0 6-2 to breeze into the second round.
Top-seeded Wozniacki, 20, needed only 60 minutes to dispose of an opponent twice her age on Monday.
The Dane now faces Canada's Aleksandra Wozniak for a place in the last 32.
Italy's reigning champion Francesca Schiavone - who beat Wozniacki in the quarter-finals last year - began the defence of her French Open crown with an easy 6-2 6-0 win over Melanie Oudin.
The fifth seed, who last year became the first Italian woman to win a Grand Slam title, suffered an early break before securing four successive games.
She needed only 62 minutes to beat the 19-year-old and plays in round two.
Third seed Vera Zvonareva overcame Lourdes Dominguez Lino and ninth seed Petra Kvitova saw off Greta Arn.
Zvonareva, who lost in the final at both Wimbledon and the US Open last year, was guilty of 29 unforced errors compared to her 30-year-old opponent's 19.
But she took the first set in 38 minutes and secured the match in an hour and 21 minutes.
Czech 19-year-old Kvitova, who lifted the recent Madrid Masters title and has been one of the stand-out performers on the women's tour this season, eased thrashed Hungary's Arn 6-2 6-1.
Top seed Caroline Wozniacki of Denmark takes on Japanese 40-year-old Kimiko Date-Krumm later on Monday.
It was an impressive start at Roland Garros for Schiavone, who racked up 25 winners to Oudin's six on Court Philippe Chatrier.
Oudin, who burst onto the tennis scene two years ago with a run to the fourth round at Wimbledon and made the US Open quarter-finals, had no answer to the strength and agility of Schiavone.
"I pretty much got a clay-court lesson," the American admitted. "Practising this past week, I haven't played anyone that hits the ball that heavy.
"She is serving well, she's moving well, she pretty much doesn't have a weakness on the clay. I can see how she won the French Open last year.
"She's so confident here. You could see the shots she was going for and making them. I thought she played really, really well. There really wasn't much I could do."
The defending champion stated: "I'm still shaking a little bit. I felt really happy to be there. The court is perfect.
"It is like when you go home and your mum does everything for you and you feel comfortable. I felt like that but with a lot of adrenaline."
Meanwhile, on Court 14 Sara Errani staged a sensational comeback to beat 18-year-old American Christina McHale.
The unseeded Italian trailed 5-0 in the deciding set but battled back to level before coming through 6-7 (4-7) 6-2 9-7.
Eleventh seed Marion Bartoli of France came back well to beat Anna Tatishvili of Georgia 1-6 6-2 6-1 and Maria Kirilenko, Russia's 25th seed beat CoCo Vandeweghe of the United States, 7-6 (7-5) 6-2.
Sixteenth seed Kaia Kanepi of Estonia beat Sofia Arvidsson of Sweden 7-5 6-1 and Peng Shuai of China beat Tamira Paszek of Austria 6-3 6-2.
There were also wins for 12th seed Agnieszka Radwanska, 28th seed Daniela Hantuchova and Roberta Vinci, seeded 30th.
But 26th seed Nadia Petrova lost to Australia's Anastasia Rodionova and 31st seed Klara Zakopalova was dumped out by Chan Yung-Jan of Taiwan.
India's Sania Mirza reached the second round for the first time since 2007 with a 6-3 6-3 win over Kristina Barrois but there was disappointment for home hope Aravane Rezai, beaten in straight sets by Romania's Irina-Camelia Begu.