Rune was booed throughout his straight-sets win over Fognini, but ahead of Thursday's second-round match against Monfils on Court Philippe Chatrier, the fiery Dane appeared untroubled by the prospect of rubbing fans up the wrong way.
"I think it's normal in life that some people love you and some people don't," sixth seed Rune told reporters after his win over Christopher Eubanks on Tuesday.
"I just try to put on a fight every time I step out there on the court. Do my best to win the match. Stay focused. I feel like to do everything I can to win the match is more important than what's happening outside the court."
Monfils, a former semi-finalist and three-time quarter-finalist at Roland Garros, opened his campaign with a five-set comeback win over Sebastian Baez.
He missed much of last season due to heel surgery, and will have his fitness truly put to the test by Rune, while needing to draw on his deep well of experience against the Dane's fast-paced all-court game.
"I'm playing full adrenaline, like honestly I asked the crowd to scream, and somehow I juice up," Monfils said after his marathon win on Tuesday.
"But I hope to have a good night today and tomorrow and heavy recovery, and no matter what, I will be ready for him Thursday (smiling)."
Elsewhere, Alexander Zverev, who exited Roland Garros in agony last year after rolling his ankle during his semi-final against Rafael Nadal, will face Slovakia's Alex Molcan.
In the women's draw, world number one Iga Swiatek's bid for back-to-back titles in Paris will be tested by American Claire Liu.
Swiatek, winner in 2020 and 2022, is a strong favourite to lift her third title at Roland Garros - which would put her on par with Serena Williams and Monica Seles - but the Pole stressed that records were the furthest thing from her mind.
"I don't even know these records. I play tennis but I'm not really an expert in terms of statistics and history, so I'm not really focused on that," Swiatek said.
"I never even played Serena or, you know, Monica Seles. So, yeah, I'm kind of living my own life and having my own journey."
Fourth seed Elena Rybakina faces Czech Linda Noskova, while seventh-seeded Ons Jabeur takes on Oceane Dodin.
