The 17-year-old wildcard survived a comeback from Paraguay’s Adolfo Daniel Vallejo to claim a remarkable 6-3, 7-5, 3-6, 2-6, 7-6 (10/8) win after four hours and 56 minutes on a raucous, and boiling hot, Court Suzanne Lenglen.
Kouame is the youngest man to reach the last 32 of a major since Nadal at Wimbledon in 2003.
Nadal went on to win 22 Grand Slam titles, including 14 at Roland Garros, and Kouame is not putting any limits on what he is hoping to achieve.
“Winning Roland Garros is, of course, a dream, but winning all four (Slams) is a dream actually, you know. Being world number one is also a dream,” Kouame, currently ranked 318th, told reporters.
“I think thinking about winning the tournament is a bit early.
“But, yeah, I’m really happy to be in the third round, as well, of course, and I’m going to try my best to win another match.”
After wins for Rafael Jodar and Joao Fonseca on Wednesday, it is the first time three teenagers have made the third round of the men’s singles at Roland Garros since Nadal, Novak Djokovic and Gael Monfils in 2006.
“I think thinking about age is a mistake,” said Kouame.
“I think because… when you are on court, you are trying to win the match. You’re not trying to think about how old is your opponent. That is something I do pretty well.”
Kouame had already become the youngest man to win a Slam match in 17 years with his first-round success against Marin Cilic.
The Grand Slam debutant powered into a two-set lead to the delight of the French fans but then started to wilt in the baking heat.
But Kouame somehow dragged himself back from the brink of defeat when Vallejo was serving for the match at 5-3 in the fifth, before completing a memorable win in a thrilling tie-break.
He soaked up the adulation from the French fans, telling them he could “never” have got over the line without them.
“I love this sport, because we get those kinds of atmospheres and for the pressure that you experience,” Kouame added.
“I was playing in front of 10,000 people, right? It’s not easy, that’s for sure, but I was able to draw into their energy because they were there to support me, not to stress me.
“But it is definitely more enjoyable to play in front of 10,000 people than 10. That’s a fact.”
Kouame will next face Alejandro Tabilo, who will be comparatively very well rested after being the beneficiary of a walkover after second-round opponent Valentin Vacherot withdrew from the tournament with an injury.