Second seed Nadal is chasing a 12th title in Paris while 2009 champion Federer, seeded three, is playing in the tournament for the first time since 2015.
Nadal starts against qualifiers in the first two rounds while 37-year-old Federer, bidding to become the oldest Grand Slam title winner of all time, faces Italy's Lorenzo Sonego, ranked at 73.
Top seed and world number one Novak Djokovic starts his campaign against Poland's Hubert Hurkacz, the world number 43.
Djokovic, the 2016 champion, is bidding to become only the second man in history to hold all four Slams at the same time.
Only Rod Laver, who swept to calendar Slams in 1962 and 1969, has previously achieved the feat.
If the seedings work out for the quarter-finals, then 15-time major winner Djokovic would face Germany's Alexander Zverev who has still to get past the last eight at a Slam.
Fourth seed Dominic Thiem, the 2018 runner-up to Nadal, would face Argentine eighth seed Juan Martin del Potro while Federer would meet Stefanos Tsitsipas, the Greek who stunned him at the Australian Open in January.
Nadal, who won his first title of 2019 in Rome last weekend against a weary Djokovic, is seeded to face Japan's Kei Nishikori in the last-eight.
In the women's draw, top seed Naomi Osaka, bidding for a third successive Grand Slam title, opens against world 92 Anna Karolina Schmiedlova of Slovakia.
However, either 2017 champion Jelena Ostapenko or two-time major winner and ex-world number one Victoria Azarenka await in a tricky second round for the 21-year-old Japanese star.
Three-time champion Serena Williams, chasing a record-equalling 24th major, begins against Vitalia Diatchenko of Russia.
Williams, seeded 10, has played just one clay court match this year. She could face Osaka in the quarter-finals in a rematch of their stormy 2018 US Open final where the Japanese star triumphed while the American suffered a spectacular meltdown.
Defending champion Simona Halep, seeded three, plays Australia's Ajla Tomljanovic in her first round match.
Venus Williams, unseeded this year, begins against ninth seed Elina Svitolina of the Ukraine.
Williams, 38, down at 52 in the world rankings, was runner-up to Serena in 2002.
Second seed Karolina Pliskova, the champion in Rome last weekend, starts against Madison Brengle of the United States.
If the seedings prove an accurate indicator, Osaka would face Australia's Ashleigh Barty in the quarter-finals, Halep would meet two-time Wimbledon champion Petra Kvitova, 2018 runner-up Sloane Stephens would tackle Madrid champion Kiki Bertens while Angelique Kerber of Germany would be Pliskova's last-eight rival.
Kerber is attempting to complete the career Grand Slam with a French Open title.