The 37-year-old, whose previous appearance at Roland Garros came in 2015, beat Italy’s Lorenzo Sonego 6-2, 6-4, 6-4 on Sunday in his first match back on the red clay in Paris to ease into the second round, Reuters reported.
The Swiss is seeded third behind Rafa Nadal and Novak Djokovic but is only fifth-favorite for the title with most bookmakers giving Austria’s Dominic Thiem and Greek sensation Stefanos Tsitsipas a better chance of victory.
“It’s nice to be an outsider. That’s how I feel, anyhow,” Federer told reporters after his win.
“This is not a show I’m putting on. This is the truth. I really don’t know how far I can go in this event, and I am very happy with my first round.
“It was a really good performance, I thought, from my side for not having played here for as long as I did.”
The 20-time Grand Slam winner, who won his only title at Roland Garros in 2009, said he is enjoying being under the radar a little bit.
“I feel like if I lost first round or in the finals or wherever it is (this year), people would be like, ‘Okay, that could have happened.’
“I like that approach for me once in a while. It relaxes you on the bigger points maybe or it relaxes you subconsciously as you walk through the grounds and go to practice and go to the press room.
“I know when Wimbledon comes around I’ll be probably a higher favorite. That’s okay, too. I’m happy with where I am.”
Federer will meet German Oscar Otte in the second round.
Defending champion Rafael Nadal, meanwhile, beat German qualifier Yannick Hanfmann in straight sets to reach the second round.
The second seed, chasing a record-extending 12th Roland Garros title, beat the world No. 180 6-2, 6-1, 6-3 on Monday.
After saving four break points in the first game, 17-time Grand Slam winner Nadal dominated throughout.
The 32-year-old won his first title since August at the Italian Open earlier in May.