Reigning women's champion Garbine Muguruza began her Roland Garros defence with a straight-sets triumph over 2010 winner Francesca Schiavone.
Nadal, who was forced to withdraw before last year's third round with a wrist injury, brushed aside 45th-ranked Benoit Paire 6-1, 6-4, 6-1 inside two hours.
"I'm very happy to be back here after what happened last year. It's great to feel the support," said the 14-time major champion.
Nadal broke Paire eight times and recovered from a slight second-set wobble when he dropped serve twice in a row to surge into a round two meeting with Dutchman Robin Haase.
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Title-holder Djokovic strolled through his opener against Marcel Granollers of Spain, advancing 6-3, 6-4, 6-2.
With 1999 French Open champion Agassi in the players box for the first time after agreeing a short-term coaching role, Djokovic experienced some trouble against the world number 77, being broken four times.
"It's great to have Andre Agassi as coach and as a mentor. I will try to learn as much as I can from him," said Djokovic.
- 'Earn confidence' -
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Muguruza's middling form this season saw her arrive in Paris with just three wins on clay, but the Spaniard dispatched former Paris champion Schiavone 6-2, 6-4.
The fourth seed will meet Estonia's Anett Kontaveit for a place in round three as Schiavone, who turns 37 in June, bid farewell to the tournament for possibly the final time.
"I cannot believe in the first round we have two ex- champions. Not only that but Francesca is a legend and I was very excited to play on Philippe Chatrier court with her," said Muguruza.
Muguruza defeated Serena Williams to win her maiden Grand Slam a year ago, but the 23-year-old needs to return to the final to stay in the world's top 10.
Canadian fifth seed Milos Raonic raced into round two with a routine 6-3, 6-4, 6-2 victory over Steve Darcis of Belgium.
Raonic, whose best run at the French Open came when he made the 2014 quarter-finals, fired 15 aces and 44 winners to book a meeting with Mikhail Youzhny of Russia or Brazil's Rogerio Dutra Silva.
Rising German star Alexander Zverev, seeded ninth, begins his campaign against veteran Spaniard Fernando Verdasco later.
The 20-year-old Zverev defeated Djokovic in Rome a week ago to become the first player born in the 1990s to land a Masters title.
Jelena Jankovic's 54th consecutive Grand Slam maiden draw appearance was a fleeting one as the three-time French Open semi-finalist was consigned to another first-round exit by Dutch qualifier Richel Hogenkamp.