Norway's Casper Ruud
Federer eased to a 6-4, 6-3, 6-4 win over German lucky loser Oscar Otte, the world number 144, to make the third round for the 15th time.
Next up for the third seed is a clash with Norway's Ruud who put out Italian 29th seed Matteo Berrettini 6-4, 7-5, 6-3.
Ruud's father Christian reached the third round of Roland Garros in 1999 when a 17-year-old Federer made his main draw debut.
Federer lost to Pat Rafter in his first round match.
According to the ATP, Christian Ruud's last career tournament was the 2001 French Open where he retired in the first round against Sargis Sargsian.
Had Ruud defeated Sargsian, he would have faced Federer in the second round.
Instead Federer came from two sets down to beat Sargsian 9-7 in fifth set to reach his first Grand Slam quarter-final.
Federer, playing in Paris for the first time since 2015 when he made the quarter-finals, hailed the fans on Court Philippe Chatrier, two of whom carried a bedsheet with 'Federer forever' painted on it.
"Thanks to the fans, a thousand times thanks."
Federer saved all four break points he faced against Otte.
"The Grand Slams are incredible. You can meet a player who qualified who (you) have not heard of before," said the 2009 champion.
"It was difficult, he really played a great match.
"Happily for me, he helped me with some mistakes at the end of the sets."