It was the Serb's 50th win at Roland Garros as he attempts to complete his collection of all four Grand Slam titles having previously won Wimbledon and the Australian and US Opens.
Flawless Nadal races into French Open second round
But it was a far from a smooth display from the 11-time major winner and three-time French Open runner-up who committed 42 unforced errors.
"He plays with a lot of speed, is good from the baseline and it was not easy for me to play the points the way I wanted," Djokovic said of 32-year-old Darcis.
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"He has a lot of talent and it was tough. I am happy to have won in three sets."
Djokovic next takes on Britain's Slovenian-born Aljaz Bedene who reached the third round of a major for the first time with a 7-6 (7/4), 6-3, 4-6, 5-7, 6-2 win over Spain's Pablo Carreno Busta.
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