Fifth seed Juan Martin del Potro struck 44 winners on his way to a 6-4 6-3 6-2 victory over French veteran Julien Benneteau, who made his final appearance at his home Grand Slam.
Big-hitting Argentine Diego Schwartzman, seeded 11th, continued his steady progress with a 6-1 6-3 6-1 win over Czech Adam Pavlasek in the second round.
Top seed Rafa Nadal, chasing his 11th title at Roland Garros, marched into the third round with a 6-2 6-1 6-1 win over Argentine Guido Pella.
Nadal will next face Frenchman Richard Gasquet who the Spaniard has beaten in all their previous 15 meetings.
World number one Simona Halep was not playing her best tennis but still found a way past American Taylor Townsend 6-3 6-1.
The Romanian, twice runner-up at Roland Garros, will meet Andrea Petkovic of Germany in the third round.
Home favourite Lucas Pouille held off a spirited comeback from Briton Cameron Norrie to beat him 6-2 6-4 5-7 7-6(3).
Pouille will next face Russian Karen Khachanov, who teamed up with the French number one for doubles action in Madrid and Rotterdam this season. Khachanov edged Pouille over three sets during their last meeting in the final at Marseille in February.
Two-time champion Maria Sharapova needed five match points to see off Croatia's Donna Vekic 7-5 6-4 in the second round. The Russian will next face sixth seed Karolina Pliskova, who beat fellow Czech Lucie Safarova 3-6 6-4 6-1.
Kyle Edmund, the last Briton standing in the singles, recovered from a mid-match blip to beat Hungarian Marton Fucsovics 6-0 1-6 6-2 6-3. Edmund will face 18th seed Italian Fabio Fognini in the third round.
Canadian teenager Denis Shapovalov was disappointed after his French Open debut ended in the second round but he remains pleased with the progress made this season.
Third seed Marin Cilic experienced a difficult test after wasting a match point in the third set against qualifier Hubert Hurkacz, but did enough to win 6-2 6-2,6-7(3) 7-5.
The Croat will next face American Steve Johnson, who also needed four sets to beat Germany's Jan-Lennard Struff.
Belgium's 16th seed Elise Mertens cruised past Britain's Heather Watson 6-3 6-4 to match her best Roland Garros performance by reaching the third round for the second year in a row.
Former champion Garbine Muguruza, seeded third, looked in fine form as she eased past French wildcard Fiona Ferro 6-4 6-3.
She moves into the third round for the fifth consecutive year, where she will face 2010 runner-up Samantha Stosur of Australia.
