Federer, the 2009 champion and hunting an 18th major, saw off Spanish qualifier Pablo Carreno-Busta, the world number 166, 6-2, 6-2, 6-3.
The 21-year-old Spaniard, who started the year at 654, boosted his ascent by winning seven Futures events and an astonishing record of 53 wins in 57 matches on the circuit's third tier.
But Federer, playing in his 15th Roland Garros, was too strong for the debutant, building the foundation for victory with a break in the opening game of all three sets.
"I didn't know a great deal about my opponent,” said the 31-year-old Federer after his 80-minute win — his 55th career victory at Roland Garros — which included 33 winners and 10 aces.
“He played really well and has a great future."
Lleyton Hewitt, like Federer a former world number one but now down at 85th in the world, put in a trademark gut-busting performance before losing a five-set thriller to French 15th seed Gilles Simon.
Hewitt had been 5-0 down in the decider and saved two match points to claw back to 5-5, but Simon just had enough stamina to achieve a 3-6, 1-6, 6-4, 6-1, 7-5 win, his first triumph from two sets to love down.
Hewitt, 32, first played Roland Garros in 1999 and was a quarter-finalist in 2001 and 2004, but had played and lost his only two previous matches on clay this year coming into Paris.
In other early matches on Sunday, Canadian 14th seed Milos Raonic defeated Xavier Malisse of Belgium, 6-2, 6-1, 4-6, 6-4 while Kevin Anderson, the 23rd-seeded South African, eased past Ukrainian lucky loser Illya Marchenko, 6-3, 7-5, 6-4.
Serena Williams, meanwhile, buried the ghosts of her 2012 French Open horror show to storm into the second round.
The 31-year-old Williams, bidding for a 16th Grand Slam title, suffered her worst defeat at a major in Paris a year ago when she was dumped out of the first round by Frenchwoman Virginie Razzano.
But on Sunday, Williams extended her current winning streak to 25, the best of her career, with a 6-0, 6-1 demolition of Georgia's Anna Tatishvili, the world number 80, who, until reaching the Strasbourg quarter-finals last week, had not won a match on the main tour in 2013.
It took Williams just 51 minutes to complete victory on a chilly Court Philippe Chatrier where the temperature hovered just above the 10-degree mark, firing 27 aces to her opponent's four.
"I am very happy, I feel very strong and I have been playing really well for the last three months," said the American.
She next faces France's Caroline Garcia who, as a raw 17-year-old, was a set up and 4-1 to the good against Maria Sharapova in 2011 before slipping to defeat.
Ana Ivanovic, the 2008 champion and 14th seed, clinched a 6-1, 3-6, 6-3 win over Croatia's Petra Martic and next faces either France's Mathilde Johansson or Chanelle Scheepers for a place in the last 32.
"The conditions were heavy and it was cold, but it wasn't an issue. It was an up and down performance," said Ivanovic.
Italian fifth seed Sara Errani, the runner-up to Sharapova last year, had the honour of being the first player to reach the second round, breezing past Dutchwoman Arantxa Rus 6-1, 6-2.
Errani needed just 54 minutes to get past world number 86 Rus, who made the fourth round in 2012, but has not won a match on the main tour this year.
The 26-year-old Errani will face highly-rated Kazakh teenager Yulia Putintseva.