Novak Djokovic has already clinched the year-end number one ranking for the sixth time as he heads into the ATP Masters starting at London's O2 Arena on Sunday.
Nadal, who claimed his 1,000th career victory by beating Feliciano Lopez on Wednesday, is bidding for a first Paris indoors triumph which would draw him level with Novak Djokovic on a record 36 Masters titles.
Paris Masters 2020: Rafael Nadal romps to 1000 Tour-level wins; Diego Schwartzman inches closer to ATP Finals debut
The 28-year-old Schwartzman was too strong for France's Gasquet, taking a 7-5, 6-3 victory, and will next face Spanish qualifier Alejandro Davidovich Fokina in the last 16 at Bercy Arena.
Humbert, who is on a seven-match winning streak after winning the Antwerp title last month, missed four match points but battled to a 7-6 (7/4), 6-7 (6/8), 7-6 (7/3) victory.
Top-seeded Djokovic lost four straight games and had to save a set point before beating Filip Krajinovic 7-6 (6), 6-3 in an all-Serbian match, and No. 2 Thiem nearly squandered a 5-1 lead in his 6-4, 7-5 win over Vitaliy Sachko of Ukraine.
French Open 2020 Round-up: Rafael Nadal eases past Mackenzie McDonald; injury forces Serena Williams withdrawal
Azarenka hit 38 unforced errors in a 6-2, 6-2 defeat against a player who hadn't won a Grand Slam match in five years before her first-round victory over Venus Williams.
French Open 2020: Andy Murray says 'difficult' to be former self but vows to 'keep going ' after Stan Wawrinka rout
Andy Murray suffered his joint-worst defeat at a major in terms of games won, succumbing to 2015 Roland Garros winner Stan Wawrinka 6-1, 6-3, 6-2 in the opening day’s marquee match of French Open.
Rafael Nadal, who is seeded second, is aiming to equal the absent Roger Federer's men's record of 20 Grand Slam titles.
Wawrinka, now 35, ranked as high as third in the world in 2014 when he won the Australian Open. He went on to win at Roland Garros the following year and the US Open in 2016.
Italian Open 2020: Teenager Lorenzo Musetti stuns Stan Wawrinka; Garbine Muguruza beats Sloane Stephens in straight sets
Stan Wawrinka, the 10th seed in Rome, lost 6-0, 7-6 (7/2) against a player ranked 249th in the world.
US Open 2020: Dominic Thiem beats Daniil Medvedev in straight sets to set up final with Alexander Zverev
The German fifth seed beat the 20th seed 3-6, 2-6, 6-3, 6-4, 6-3 in 3hr 23min inside Arthur Ashe Stadium to set up his first ever Grand Slam final.
Prague ATP Challenger: Stan Wawrinka beats Russia's Aslan Karatsev in straight sets to win tournament
Wawrinka, the 2016 US Open winner, has elected to skip this year's Grand Slam in New York citing the "health situation" in the city and instead focus on Roland Garros which starts on September 27.
Nagal had also taken a set off another Swiss star and multiple Grand Slam winner Roger Federer in the US Open last year before losing the match.
US Open 2020: Former champion Stan Wawrinka confirms he's skipping tournament due to 'health situation in New York'
Wawrinka, the US Open winner in 2016, was already missing from the entry list along with four-time champion Rafael Nadal.
'Gambler' Stan Wawrinka is underestimated, can beat anyone from the Big Four on his day, says his coach Magnus Norman
Wawrinka, 35, was the last man to win a Grand Slam singles title outside the trio of Roger Federer, Rafael Nadal and Novak Djokovic when he won the 2016 US Open.
Firstpost Masterclass: Rohan Bopanna breaks down intricacies, technique behind much-loved single handed backhand
In this edition of Firstpost Masterclass, Bopanna breaks down the single handed backhand, the technique behind it, how it differs from surface to surface, the love affair that fans have with it and much more.
World No 6 Stefanos Tsitsipas says his claim of being 'really close' to winning a Grand Slam was too big a statement
The 21-year-old Tsitsipas is ranked number six in the world and had announced he was “really close” to being crowned a Grand Slam champion after his triumph in the ATP Finals last year
Coronavirus crisis forces sportspersons to contemplate playing behind closed doors while chess and poker go online
The coronavirus pandemic has pushed hyperactive sportspeople, used to living out of suitcases, to grapple with adjusting to the new normal, which is to stay at home and maintain fitness.
Coronavirus Outbreak: Novak Djokovic, Roger Federer, Rafael Nadal discuss fund to help lower ranked players
Novak Djokovic says he spoke with Roger Federer and Rafael Nadal about working with the ATP to set up a fund to help lower-ranked tennis players financially affected by the coronavirus pandemic.
Tokyo Olympics 2020 getting postponed until 2021 may be a blessing for tennis calendar ravaged by coronavirus
Tennis has also been impacted by the flu-like disease that has killed more than 17,200 people worldwide since emerging in China late last year.