The Argentine's first four outings at the majors all ended in first round defeats but this year he has shown improvement.
After a third round showing at the Australian Open, he has now gone one better but dismissed suggestions that he could soon be breaking into the top 10.
"I don't feel like I belong in the top 10 because I'm not even in the top 20," the 23rd seed told reporters.
"I think I'm going to be in the top 20 or probably close to that next week. I'm working to get to that level. I'm closer, but I have to keep going, keep winning and keep improving. So hopefully one day I can be among those top 10 players."
Cerundolo frustrated Fritz with his sharp baseline game to complete victory on Court Suzanne-Lenglen after two hours 50 minutes.
"It was a very tough match. He's a Top 10 player. I knew what kind of match it was going to be," he added.
"The first set was a bit tense. I didn't play well. After that, I started to play better, more aggressive, less mistakes. But, of course, it was a great battle."
Cerundolo, a quarter-finalist at the ATP Masters 1000 events in Miami and Rome this season, will continue his Roland Garros campaign against sixth seed Holger Rune (20) on Monday.
"I played against him in 2019, I think in a Challenger. But now he's a top-10, top-five guy. He did amazing this last week. Final in Monte Carlo and Rome, title in Munich. He's a great clay-court player, so it's going to be a tough match.
"I hope I can play at the level I've been playing the last few days, because I think I have my chances. I'm going to focus on my game and try to play my best and get the win," he added.
