World number one Djokovic and Nadal, ranked five, are seeded to meet as early as the quarter-finals.
Alcaraz, 19, is bidding to become just the eighth teenager to win a Grand Slam men’s title.
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He could face either Djokovic or Nadal, who holds a record 21 majors, in the semi-finals in a top-heavy draw for the second Grand Slam of the season.
“I am very motivated to play my best tennis,” said two-time French Open champion and 20-time major winner Djokovic.
“In Paris, I always play very strong. Last year, it was the toughest major that I had won.”
Djokovic had to twice come from two sets down last year to beat Lorenzo Musetti in the last-16 and Stefanos Tsitsipas in the final having also beaten Nadal from a set behind in a bruising semi-final.
“Musetti, Rafa, Tsitsipas — every match lasted more than three hours, a lot of sets. It was exhausting but I loved the outcome.”