Nadal, the record 14-time champion at Roland Garros, is unseeded this year after injury saw his ranking plummet to 276.
He and Zverev met in the semi-finals of the French Open in 2022 when the German was forced to retire after suffering a serious ankle injury.
Nadal, the winner of 22 Grand Slam titles, will turn 38 next week and this season will be his last on tour.
He holds a 7-3 winning head-to-head record against Germany's Zverev with five of those victories coming on clay.
Zverev, 27, arrives in Paris on the back of lifting the Rome Open title last weekend.
Swiatek and Osaka in potential second-round clash
Defending champion Iga Swiatek and fellow four-time Grand Slam title winner Naomi Osaka could clash in the French Open second round after the draw was made on Thursday.
Top seed and world number one Swiatek will take on a qualifier in her opener with Osaka facing Lucia Bronzetti of Italy in her first-round tie.
Swiatek is bidding to win a fifth major and fourth French Open title.
"It feels like home here," said Swiatek who arrives at the tournament with clay-court titles in Madrid and Rome under her belt.
"I have been working hard to play at a high level."
Former world number one Osaka, now ranked 134, has never got past the third round in Paris.
Bronzetti, the world number 48, has yet to win a main draw match at Roland Garros in two visits.
Osaka, 26, has endured a bittersweet relationship with the French Open.
In 2021, she was fined for opting out of mandatory media commitments before withdrawing from the competition after just one match insisting she was protecting her mental health.
Osaka missed the 2023 edition due to being pregnant before giving birth to a baby girl in July.
Swiatek, meanwhile, is bidding to become the first player to lift three successive women's titles in Paris since Justine Henin in 2007.
The 22-year-old Pole is also aiming to join Chris Evert, Steffi Graf and Henin in lifting the Coupe Suzanne-Lenglen four times in the Open era.
Click here for the full men's and women's draw for Rolland Garros.
