The second-seeded former world No. 1 handled Bosnian Damir Dzumhur, 10 years the Swiss great's junior, 6-4, 6-3, 6-2 on the famed red clay on Court Chatrier.
The 33-year-old Federer is through to the fourth round at Roland Garros for the 11th straight year. He completed the career Grand Slam when he lifted the trophy in 2009, beating Robin Soderling in the final.
The world No. 88 Dzumhur was contesting the third round of a Grand Slam for the second time, having also reached the last 32 at the this year's Australian Open as a qualifier.
In addition to the title, the 17-time Grand Slam king Federer has lost to Rafael Nadal in four finals at Roland Garros.
Another third-round result saw Russian journeyman Teymuraz Gabashvili douse Czech Lukas Rosol 6-4, 6-4, 6-4.
The second round concluded when 20th-seeded Frenchman Richard Gasquet held off Argentine Carlos Berlocq 3-6, 6-3, 6-1, 4-6, 6-1 in a match that was suspended after four sets on Thursday because of darkness.