Gasquet reached the quarter-finals for the first time at the 13th attempt with an upset win over fifth seed Kei Nishikori on Sunday.
After four fourth-round defeats on his last five appearances at his home grand slam, it was a landmark achievement and one celebrated exuberantly by the crowd on Court Philippe Chatrier.
But history does not favour Gasquet going any further. One of those fourth-round defeats was against Murray, when the Scot came from a set down to win in 2012.
His only defeat by a Frenchman at Roland Garros, meanwhile, came a decade ago against Gael Monfils when he was still a teenager.
Murray said: “I’m pumped to be in the quarters of a slam. Obviously the atmosphere will be tough but I don’t mind that.
“I’ve played a number of times against French players here in difficult atmospheres and I managed okay. So I’m sure I’ll be fine.”
Playing the role of pantomime villain appeals to Murray’s contrary nature and he walked onto court for the 2012 clash with Gasquet to a chorus of boos and with a big grin on his face.
The 29-year-old needs to be fired up to play his best tennis and that was fully in evidence in his fourth-round win over John Isner, when he berated himself constantly but played a fine match to win in straight sets.
Beating big servers Isner and Ivo Karlovic has allowed him to recover physically from his five-set battles in the opening rounds, which is crucial because major tests await.
If he can get past Gasquet and his flowing backhand, defending champion Stan Wawrinka is likely to be waiting, while Novak Djokovic looks to have a comfortable path to the final on the other side.
Murray said: “I feel fine now. Between now and the end of the tournament, it’s completely different matches (to Karlovic and Isner). A lot more rhythm, longer points, more physical matches.
“So I’ll need to change the way I’m playing a little bit and make some adjustments for those matches.”
Murray and Gasquet have known each other since their junior days, when the Frenchman was considered the leading talent.
But he has never managed to reach the same level as the likes of Murray, Djokovic and Rafael Nadal, hindered by both physical and mental frailty.
He is expecting neither from Murray, saying: “He’s a huge fighter. He runs all over the place. You never get a free point. He has a very powerful mind.
“When the point is important, he serves fast, he sends it back, physically he’s perfect. He’s a big competitor. And he always hangs in there and wins these matches.
“He had a surprisingly difficult start to this tournament. But he played very well in Rome and Madrid. He’s the number two player, and for good reason. Because he’s a great player.
“We have played together very often. He’s always defeated me in the grand slams, but I’d like to change the tide.”
The pair’s biggest opponent may be the weather, and it is doubtful whether they will be able to complete on match on Tuesday as scheduled.
Murray, meanwhile, revealed he will seek medical advice about the Zika virus before committing to the defence of his Olympic title, although he stressed he is planning to play in Rio.
Several leading players, including Isner and 15th-ranked Dominic Thiem, have decided not to play, but not for reasons of health so much as the lack of ranking points and prize money.
Murray, who frequently cites winning Olympic gold in London as the best moment of his career, said: “The reason I’m playing there is to try and win medals.
“I know how special that week was for me, so that’s why I obviously commit to playing the Olympics. I don’t understand why some of the players don’t want to play.
“There are different reasons for playing tournaments sometimes and, for me, Davis Cup and Olympics, I’m not playing for ranking points.”