Two years ago at Wimbledon in 2014, Kyrgios gained worldwide attention by saving nine match points in the second round and defeated Gasquet 10-8 in the final set by coming back from two sets to love down.
The ninth-seeded Frenchman will have the French crowd firmly behind him but this will be an atmosphere which the young Australian will thrive on.
Gasquet is one of four seeded Frenchmen along with Jo-Wilfried Tsonga, Gilles Simon and Jeremy Chardy to be in the third round at Roland Garros, flying the flag high for France as they are on their quest for a Frenchman to win the title in Paris for the first time since Yannick Noah in 1983.
How they got here
Kyrgios has been playing scintillating tennis at the French Open and in his first round match on Sunday before the rain distrupted play on Court One, Kyrgios was able to finish off his match against Italy's Marco Cecchinato which he won 7-6, 7-6, 6-4.
In his second round match, he dispatched Dutchman Igor Sijsling 6-3, 6-2, 6-1 in an impressive one hour and 10 minutes to reach the third round.
Meanwhile for Gasquet, he hasn't dropped a set also and defeated Thomaz Bellucci 6-1, 6-3, 6-4, which many people tipped that Gasquet could be the first top 10 seed to fall at the French Open in the opening round and in his second round match, Gasquet defeated American wildcard Bjorn Fratangelo 6-1, 7-6, 6-3.
Gasquet and Kyrgios have met each other six times and the French veteran leads their head-to-head 4-2 with Gasquet winning twice on clay, once on grass and once on hard. Kyrgios' two victories over the Frenchman have been on grass and clay.
The pair's first meeting was during the first round of the Davis Cup in 2014 in France which Gasquet won 7-6, 6-2, 6-2 and their second meeting was a historic one as Kyrgios at 19 years old, was victorious on Court 2 at Wimbledon.
Kyrgios followed up that win by defeating former world number one Rafael Nadal in the fourth round to reach his maiden Grand Slam quarterfinal.
Gasquet won all three of their meetings in 2015 starting with a win in the final in Estoril and the ninth seed gained his revenge at Wimbledon on the same court by defeating Kyrgios in four sets with a 7-5, 6-1, 6-7, 7-6 scoreline.
The Frenchman defeated Kyrgios in their opening round match at the Western and Southern Open in Cincinnati with a comprehensive 6-2, 6-1 scoreline which the Aussie was accused of tanking.
They have met already once this year in France but in Marseille in the quarterfinals, Kyrgios won 6-0, 6-4 en route to his maiden ATP title.
If Nick Kyrgios can have a clear head and not get caught up with the crowd cheering for Gasquet, Kyrgios will have a very good chance on advancing to the fourth round of the French Open for the first time.
Gasquet is used to playing Kyrgios now and he will be able to retrieve his booming serves which isn't as affective on a clay court but it is still a dangerous weapon and he will still need to be wary.
The winner of this match will have a tough fourth round encounter with either fifth seed Kei Nishikori or Fernando Verdasco.
This match is scheduled third on Court Philippe Chatrier and you will expect the stadium to be packed to the rafters.
Prediction: Nick Kyrgios to win in four sets.