Djokovic is chasing a record 23rd men's Grand Slam title in the absence of the injured Rafael Nadal, who will miss the tournament at Roland Garros for the first time since his 2005 title-winning debut.
The third-seeded Djokovic, Roland Garros champion in 2016 and 2021, meets 114th-ranked Aleksandar Kovacevic of the US in the first round in Paris -- the first French Open since 1998 without Nadal or the now retired Roger Federer.
The 24-year-old Kovacevic is making his Grand Slam main draw debut.
Djokovic, who turned 36 on Monday, has been bothered by a recurrence of a right elbow injury which has disrupted his clay-court season.
He failed to go beyond the last eight at any of the three events he played on clay this spring, losing his number one spot to Alcaraz.
Djokovic has also fallen behind Daniil Medvedev in the rankings after the Russian succeeded him as Italian Open champion last weekend.
US Open champion Alcaraz and Medvedev both start their Roland Garros campaigns against a qualifier or lucky loser.
Alcaraz is also on track to play 2021 French Open runner-up Stefanos Tsitsipas in the quarter-finals.
Reigning women's champion Iga Swiatek begins her title defence against Spain's Cristina Bucsa, the world number 67 who was beaten by the Pole in the third round of this year's Australian Open.
The top-ranked Swiatek, bidding to become the first back-to-back women's champion at the French Open in 16 years, is coming off a thigh injury which forced her to retire in Rome.
She is seeded to meet 2022 runner-up Coco Gauff in the quarter-finals and could face Wimbledon champion Elena Rybakina, last week's Italian Open winner, in the last four.
"This is my favourite tournament. I always get this extra motivation to practise harder here. I'm really excited to be here," Swiatek said during the draw ceremony.
Aryna Sabalenka, who won her maiden Grand Slam crown in Melbourne, plays Marta Kostyuk of Ukraine in round one. Sabalenka has never got beyond the third round in Paris despite making at least the semi-finals at all of the other three majors.
Third seed Jessica Pegula has a tricky opening match against fellow American and 2022 Australian Open finalist Danielle Collins, while Rybakina gets a qualifier or lucky loser first up.
Ons Jabeur, seeded seventh, is a potential quarter-final opponent for Rybakina, who defeated the Tunisian in the 2022 Wimbledon final. Jabeur also finished runner-up to Swiatek at the US Open.