Women’s second seed and former finalist Coco Gauff booked a place in the last 32, after 18-year-old contender Mirra Andreeva cruised through.
World number one Sinner had no trouble in seeing off the 38-year-old Gasquet, playing at the tournament for the 22nd and final time, 6-3, 6-0, 6-4 in under two hours.
Sinner made his comeback from a three-month doping ban at the Italian Open earlier in May, reaching the final before losing in straight sets to reigning Roland Garros champion Carlos Alcaraz.
He was in fine form against Gasquet, saving three break points to serve out the first set before dominating the rest of the match on Court Philippe Chatrier.
“Thank you for being very fair with me today, I know what was at stake,” Sinner told the crowd after setting up a third-round meeting with Czech Jiri Lehecka. “It’s your (Gasquet’s) moment. Congrats on an amazing career.”
Djokovic continued his bid for a record-breaking 25th Grand Slam title by downing Frenchman Corentin Moutet in straight sets, despite needing a medical time-out to treat apparent blisters on his foot.
The 38-year-old, who became just the third man to win 100 ATP titles last week in Geneva, eventually put away an obdurate Moutet, winning 6-3, 6-2, 7-6 (7/1) after three hours and five minutes.
The Serb will next play either Canadian 27th seed Denis Shapovalov or Austrian qualifier Filip Misolic, as he edges closer to a possible quarter-final clash with Alexander Zverev.
“I think in general I played well,” Djokovic said after an impressive display against an awkward opponent who missed a set point in the third.”
“I came to Roland Garros with more confidence, good feelings,” he added. “Hopefully I can continue like that.”
Third seed Zverev bounced back from losing the first set in a 3-6, 6-1, 6-2, 6-3 win over Dutchman Jesper de Jong.
The German, who lost last year’s final to Alcaraz in five sets, will next face Italian Flavio Cobolli on Saturday for a last-16 berth.
Australian ninth seed Alex de Minaur’s run of reaching four consecutive Grand Slam quarter-finals was ended as he blew a two-set lead to lose 2-6, 2-6, 6-4, 6-3, 6-2 to Alexander Bublik.
Czech teenager Jakub Mensik, the Miami Open champion, also suffered a collapse from two sets up in a 2-6, 1-6, 6-4, 6-3, 6-3 defeat by Grand Slam debutant Henrique Rocha of Portugal.
Home hope Arthur Fils narrowly avoided suffering a similar fate though.
The 14th seed fought back from a break down in the deciding set to grab a dramatic 7-6 (7/3), 7-6 (7/4), 2-6, 0-6, 6-4 victory over Spaniard Jaume Munar on a raucous Court Suzanne Lenglen despite battling a back injury.
Brazilian teenager Joao Fonseca reached the third round of a Grand Slam event for the first time with a straight-sets win against French wildcard Pierre-Hugues Herbert.
The 18-year-old will next face the winner of the night session match between Gael Monfils and British fifth seed Jack Draper.
Gauff struggled with her serve but did enough to claim a 6-2, 6-4 win over 2024 French Open girls’ champion Tereza Valentova.
She only managed one hold of serve in a scrappy second set but broke her 18-year-old Czech opponent eight times in the match to secure a third-round meeting with Marie Bouzkova.
The American is targeting a first title since last year’s WTA Finals, having come up just short in Madrid and Rome.
“I could have been more aggressive on serve but the return game was good,” Gauff said.
Sixth seed Andreeva, who had an impressive run to the semi-finals at Roland Garros last year, brushed side American Ashlyn Krueger 6-3, 6-4.
Andreeva is playing her first Grand Slam as a top-10 seed after capturing WTA 1000 series titles in Dubai and Indian Wells.
“I’m just happy that I stayed calm during the match, and I’m happy that I overcame some little difficulties throughout the match,” said the Russian.
Third seed Jessica Pegula beat fellow American Ann Li 6-3, 7-6 (7/3) and will face former Wimbledon winner Marketa Vondrousova in the third round.
Madison Keys, who won her maiden Grand Slam title at the Australian Open in January, saw off Katie Boulter 6-1, 6-3.
Reigning Wimbledon champion Barbora Krejcikova was knocked out, though, dispatched 6-0, 6-3 by Russian Veronika Kudermetova. (AFP)
