The second-seeded Serb was leading 4-1 when rain halted play on Court Philippe Chatrier, but it restarted about an hour later.
"Very heavy conditions. The court is not that great, in a great condition, at this moment," Djokovic said. "But of course, considering the amount of the rain that we had in last four or five days, it is not easy for people to maintain the court in the right state. They are doing their best."
In the second set, a short shower stopped play for only a few minutes. Djokovic, wearing a white rain jacket, used the time to entertain the crowd by chatting with a ball boy and letting the youngster sit alongside him on the bench.
At one point, Djokovic grabbed the umbrella out of the ball boy's hand and in return gave him a racket. Then Djokovic handed him a bottle of Perrier, and the two clinked bottles before taking a sip.
"We had a nice chat. He's a tennis player, so I asked him how long he's playing, and how he's enjoying his time as a ball kid," Djokovic said. "It was a nice, fun time, something unusual for the Grand Slams."
Djokovic can complete a career Grand Slam by winning the French Open.
Nadal has already won a record eight French Open titles, but he is looking to become the first man to win five times in a row in Paris.
On Monday, he improved his record at Roland Garros to 60-1 by beating Robby Ginepri of the United States 6-0, 6-3, 6-0.
Sharapova, the 2012 champion, was first on court in the main stadium and needed little more than an hour to beat Ksenia Pervak 6-1, 6-2.
"It's always nice to get out there on a day like this. It's good to play first match, as you know," Sharapova said. "Hopefully you'll be able to finish the match today with the weather conditions being as they are. It's always nice to get through."
Sharapova broke Pervak five times and finished with 17 winners, while Pervak had only four.
Sharapova, seeded seventh at the French Open, completed a career Grand Slam at Roland Garros two years ago. She then lost to Serena Williams in the 2013 final.
Up next in Paris will be Tsvetana Pironkova of Bulgaria in the second round. But she could face Williams in the quarterfinals.
"It's tough to think about that match down the line where you have to compete in three matches before that," Sharapova said. "Obviously it's a match that many people always look forward to when we play against each other."
Monday's match started about 1 hour, 20 minutes late because of the wet weather. The forecast calls for more rain for the rest of the week.
Australian Open runner-up Dominika Cibulkova of Slovakia also advanced, beating Virginie Razzano of France 7-5, 6-0.
Other winners include No. 12 Flavia Pennetta of Italy, No. 16 Sabine Lisicki of Germany, No. 17 Roberta Vinci of Italy, No. 18 Eugenie Bouchard of Canada, No. 19 Samantha Stosur of Australia, No. 20 Alize Cornet of France and No. 32 Elena Vesnina of Russia.
On the men's side, ninth-seeded Kei Nishikori was knocked out in the first round, losing to Martin Klizan of Slovakia 7-6 (4), 6-1, 6-2.
Nishikori won his first clay-court title in Barcelona last month. He then reached the final in Madrid but had to retire with a back injury against Nadal.
Nishikori, the highest-ranked Japanese man in history, is No. 10 in the world, one spot lower than his career high.
No. 17 Tommy Robredo of Spain, No. 25 Marin Cilic of Croatia, No. 26 Feliciano Lopez of Spain, No. 27 Roberto Bautista Agut of Spain and No. 29 Gilles Simon of France advanced, while No. 30 Vasek Pospisil of Canada lost.
Later Monday, Australian Open champion Stan Wawrinka was playing Guillermo Garcia-Lopez of Spain on center court.