Djokovic, who won the event at Roland Garros in 2016, secured a 6-1, 6-4, 6-3 win on Court Suzanne Lenglen in Paris. He knocked out Henri Laaksonen, who was previously beaten by Mikael Ymer in the third round of qualifiers but continued on as a "lucky loser" following withdrawals.
Laaksonen defeated Pedro Martinez in the opening round to set up his first match against Djokovic. The Serbian, the No. 1 seed in the tournament, won the first set in only 23 minutes as he cruised to a straight-sets victory.
No. 4 seed Dominic Thiem, who was the runner-up in the French Open last year, edged Alexander Bublik with a 6-3, 6-7 (6), 6-3, 7-5 win.
Bublik attempted to disrupt Thiem with underarm serves but couldn't beat the Austrian, who takes on Pablo Cuevas in the next round.
"He made my life on the court very tough," Thiem told reporters. "He [did] many things which are not easy for my game. So it was a really strange and difficult four sets for me. I'm happy I didn't have to go to a fifth. ... Really happy to be through."
In other men's action at the French Open, fifth-seeded Alexander Zverev won in three sets against Ymer. The German posted a 6-1, 6-3, 7-6 (7) victory, putting the top seven seeds in the third round.
Salvatore Caruso picked up a dominant 6-1, 6-2, 6-4 win over No. 26 Gilles Simon. No. 17 seed Diego Schwartzman lost 4-6, 6-3, 6-4, 7-5 to fellow Argentine Leonardo Mayer.