The two will clash tomorrow with a spot in the fourth round – and a likely showdown with in-form fifth seed Kei Nishikori – on the line.
And while Kyrgios continues to attract criticism over his potential Olympic selection – swimming great Kieren Perkins the latest to argue against the 21-year-old heading to Rio – Gasquet leapt to his young rival’s defence.
“He has a very strong personality. That’s great. It’s good to have players like him,” Gasquet said following his straight sets drubbing of Bjorn Fratangelo.
“Outside of the court he’s very respectful. He’s a guy I like very much.
“Every time I’ve played him things went very well. I think we are all quite lucky to have a guy like him on the tour.”
Kyrgios came under heavy criticism for his slanging match with respected match umpire Carlos Ramos following what the Canberran labelled a tough code violation for shouting for a towel from a ball boy.
Tournament officials agreed the on-court punishment of a warning was sufficient and Kyrgios escaped a fine.
Whether Gasquet will escape with a win in front of his home fans is another matter.
While he holds a 4-2 advantage in their head-to-head record, including victories in their only two matches on clay, the Frenchman says Kyrgios is a more dangerous proposition than ever before.
“He’s made some progress this year. He’s stronger than last year,” Gasquet said.
“He’s won some big matches … he’s done great things. He’s a great player.
“He’s the best newcomer coming now, so it will be an incredible match for me.”
Australia’s top-ranked male and female players, Kyrgios and Samantha Stosur, waltzed into the third round overnight but wildcard Jordan Thompson suffered a heartbreaking exit in his Roland Garros debut.
After courting controversy in his opening win on Sunday, Kyrgios kept his nose clean against a hopelessly outclassed world No.123 Igor Sijsling overnight, winning 6-3 6-2 6-1.
Stosur, too, advanced with relative ease – breaking her Chinese doubles partner Shuai Zhang five times in her 78-minute 6-3 6-4 victory.
Stosur will next face 11th seed and last year’s runner-up Lucie Safarova on Friday.
Kyrgios finished with a ripping backhand – one of 35 winners from his racquet.
He also won five breaks of serve and closed out the match in 70 minutes – faster even than Rafael Nadal’s 80-minute demolition of Australian Sam Groth on Tuesday.
“You don’t really see too many of those matches go that quick, but I thought he was really aggressive from the get-go,” Kyrgios said.
“Every forehand he had he was trying to really pull the trigger.
“I didn’t feel he felt comfortable extending the rallies.
“I thought there was going to be a lot more rallies today (but) I served well and I returned well. I just played good tactical tennis.”
The 17th seed will next face French nemesis Richard Gasquet, after he enjoyed a breezy straight-sets win over American Bjorn Fratangelo.
Thompson, meanwhile, was outlasted in a five-set epic by the 37-year-old 27th seed Ivo Karlovic of Croatia 6-7 (2-7) 6-3 7-6 (7-3) 6-7 (4-7) 12-10 in four hours and 31 minutes.
He was seeking to become just the second Australian wildcard to reach the French Open third round, following in the footsteps of Thanasi Kokkinakis last year.
But he fell in cruel fashion as Karlovic sent down a tournament-high 41 aces.
Thompson incredibly saved triple break point in the 15th game of the fifth set to hold serve – where a break would have allowed Karlovic to serve for the match.
It proved to no avail, however, as Karlovic eventually broke him with a deep backhand winner in the 21st game and all Thompson could do was stare at the sky before Karlovic sent down three aces to serve out the match.
Bernard Tomic plays his second-round match against Borna Coric tonight, Australian time.
Meanwhile, there was Australian carnage among the doubles matches, with John Millman, Bernard Tomic, Sam Groth and the Rodionova sisters, Arina and Anastasia, all suffering defeats.
Groth and Tomic teamed up but were no match for the French top seeds Nicholas Mahut and Pierre-Hughes Herbert, who won 6-3 6-3.
John Peers and his Finnish partner Henri Kontinen, however, survived their first-round clash with Spanish duo Nicholas Almagro and Guillermo Garcia-Lopez, winning 6-7 (6-8) 6-4 7-6 (7-3).
Veteran left-hander Chris Guccione also advanced with his Brazilian partner Andre Sa, downing Colombian 13th seeds Robert Farah and Juan Sebastian Cabal.
HOW THE AUSTRALIANS FARED ON DAY THREE OF THE FRENCH OPEN (Prefix denotes seeding:)
Men’s singles, second round
17-Nick Kyrgios bt Igor Sisling (NED) 6-3 6-2 6-1
Jordan Thompson lost to 27-Ivo Karlovic (CRO) 6-7 (2-7) 6-3 7-6 (7-3) 6-7 (4-7) 12-10
Women’s singles, second round
21-Samantha Stosur v Shuai Zhang (CHN) 6-3 6-4
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