The world number one got off to a flyer in the opening set and looked likely to take full control of the match while Kavcic struggled to make any sort of impact in the first 20 minutes.
Djokovic snatched a one-set lead with ease while his Slovenian opponent failed to put one game on the score board.
Despite a strong start, the Serbian professional experienced a slight dip in the initial stages of the second set as Kavcic managed to take a hold in the game and get his first points on the board.
While Kavcic showed signs of improvement, it wasn't enough to harm Djokovic, who grabbed a vital break of serve and went on to take a two-set lead in Paris.
Djokovic, who has yet to win the French Open, held his serve well in the third set but his 25-year-old opponent put up a fight and managed to retain his serve and prevent the top seed from snatching the breakthrough.
Despite a late struggle, Djokovic was successful in securing the third and taking the match in straight sets.