The top seed had to wait until the night match on the third day of the tournament to begin his quest for a record-extending 25th Grand Slam title but quickly hit his stride to dispatch French wild card Herbert on Court Philippe Chatrier.
Djokovic has not reached a final this year and his world No 1 ranking is under threat from Jannik Sinner.
He said he arrived at Roland Garros with “low expectations and high hopes” after suffering some uncharacteristic defeats this year.
But everything looked in fine working order against Herbert who put up solid resistance but never looked likely to unduly concern the Serbian who has now won 72 of his 74 first-round matches in Grand Slam tournaments.
The only moment of slight drama came deep in the third set when Djokovic took a nasty tumble down by the net, and was booed by the ever-friendly Paris crowd as he towelled himself down.
