Federer equalled Jimmy Connors's record of 233 grand-slam match wins with a 6-2 7-5 6-3 defeat of German Tobias Kamke, the first step, he hopes, on the road to a record 17th title at one of the big four tournaments.
Djokovic, though, has a record of his own on his mind and, after a mostly straightforward, 7-6 6-3 6-1 win over Italian Potito Starace, turned his thoughts towards trying to complete his grand-slam collection and becoming the first man in 43 years to hold all four titles at once.
"The situation that I found myself in this year before Roland Garros is to make history eventually if I go all the way through," Djokovic told a news conference.
"But, look, it doesn't give me an extra negative pressure; I really think it's a challenge and something to embrace and to enjoy."
Djokovic will now play Blaz Kavcic of Slovenia, who ended former U.S. Open and Wimbledon champion Lleyton Hewitt's tournament with a 7-6 6-3 6-7 6-3 win after the injury-hit Australian had been given a wildcard.
Federer took time to look back on his long career as he began his 50th consecutive grand slam event.
"I obviously love the big tournaments," the Swiss said. "I have been so successful for such a long time and to already tie that (Connors's) record, (at) 30 years old is pretty incredible, so I'm very happy.
"When you look at the tournaments like this and you step back, you realise you have been playing for quite a long time.
"When I started, I loved playing against those famous players I used to see on TV. Now I'm playing against younger players, a new generation. It's also very nice."
Federer, on course to meet Djokovic in the semi-finals if both men survive, will now meet Adrian Ungur of Romania, who knocked out Argentine David Nalbandian 6-3 5-7 6-4 7-5.
MISERABLE MOMENT
Victoria Azarenka also had much to chew over after coming within five points of going down in the record books as the first women's top seed to lose in the opening round of the claycourt grand-slam event.
Thoughts of flights home to Minsk flitted through her mind at 6-7 0-4 down against Italian Alberta Brianti, 10 years her senior at 32, the Belarussian admitted.
"The important thing in that really miserable moment, I stayed strong and I just went for my shots," Azarenka added after turning the tide to win 6-7 6-4 6-2.
One-sided victories in the sunshine by defending champion Li Na and third seed Agnieszka Radwanska flagged up the lack of depth in women's tennis with both players detained on court for less than an hour.
Li, a superstar at home in China after last year's Roland Garros win, beat Romania's Sorana Cirstea 6-2 6-1, while Pole Radwanska showed even less mercy, thrashing Serbian Bojana Jovanovski 6-1 6-0.
Frenchwoman Marion Bartoli, buoyed up by the crowd on the Suzanne Lenglen Court, was also a swift winner, defeating Czech qualifier Karolina Pliskova 6-3 6-3.
Radwanska's second-round task will be an interesting match-up with former world number one Venus Williams, though the American is the first to admit that she is still searching for her old form after being diagnosed with a fatigue-inducing illness.
The tournament lost women's 11th seed Vera Zvonareva of Russia and men's number 15 Feliciano Lopez of Spain to injury, while local hero Arnaud Clement collected an unusual win when his Russian opponent Alex Bogomolov Jr retired at matchpoint down because of severe cramp.
Defending champion Rafa Nadal enters the fray on Tuesday, when former women's singles winner Serena Williams and world number two Maria Sharapova also have their first-round ties.
