On court, however, Nadal is absolutely ruthless with his childhood friend. Juan Martin del Potro was a victor over former quarterfinalist ALbert Ramos Vinolas 7-5, 6-4, 6-1.
The pair were regarded as two of the best young players of their generation as juniors, but Nadal has won 16 Grand Slam titles while Gasquet has never reached a final at the majors.
Marin Cilic has moved into the fourth round at a Grand Slam tournament for the 20th time, eliminating Steve Johnson of the US 6-3, 6-2, 6-4.
They have played 10 times, with del Potro leading, 6-4, in their head-to-heads dating to 2008.
Goffin led by a break in the third set with the score at one set apiece overnight, only for Monfils to roar back and win the third set.
Isner served 12 aces but fell short of becoming the first American man to reach the quarterfinals since Andre Agassi in 2003.
The 31-year-old Russian, seeded 28th after missing this tournament the last two years, needed 59 minutes to win on Court Philippe Chatrier.
Williams announced her withdrawal at a news conference at Roland Garros on Monday. And he did on the anniversary of the Swiss' iconic win in Paris against him.That win sealed one of the best matches ever played in this sport's history and made Federer stop the Serb's remarkable unbeaten run at 43 consecutive matches.
Sixth seed Kevin Anderson is a potential quarter-final opponent for Nadal after beating Mischa Zverev 6-1 6-7 (3-7) 6-3 7-6 (7/4).
The No. 3-seeded Croat won the 2014 U.S. Open and has reached the final at two of the past three majors - Wimbledon a year ago and the Australian Open in January.
Diego Schwartzman joined countryman del Potro in the fourth round with an impressive 7-5, 6-3, 6-3 victory over Borna Coric. Marco Cecchinato abide, being the ninth Italian to reach the last 8 here, he who hasn't won a single Grand Slam main draw match before this week. He'll next face No 11 seed Diego Schwartzman, a 7-5, 6-3, 6-3 victor against Borna Coric.
From being on the precipice of defeat when serving at 4-5 in the fourth set, the eighth-seeded Belgian then profited when Monfils lost his cool with the umpire after a warning for taking too much time between points.
Top seed and Romanian tennis ace Simona Halep and Russia's Maria Sharapova comfortably beat their opponents and progressed to the third round of the French Open here on Thursday.
The Croat will face Italy's Fabio Fognini, who knocked out British number one Kyle Edmund as he took a thrilling five-setter 6-3 4-6 3-6 6-4 6-4.