Spain’s Nadal, who has won the men’s title on a record 14 occasions, plans to retire later this year.
Zverev, 27, is one of the favourites for the title and tuned up by winning the Italian Open last week.
Britain’s Andy Murray has also indicated he will call it a day in the coming months and starts against fellow veteran Stan Wawrinka.
Defending men’s champion Novak Djokovic starts against French wildcard Pierre-Hugues Herbert, while Iga Swiatek begins her bid for a third women’s title in a row against a qualifier or lucky loser.
The French Open, which is the second Grand Slam tournament of the season, starts on Sunday.
While world number one Swiatek is the overwhelming favourite for the women’s singles, Aryna Sabalenka is expected to be the player who could end her clay-court dominance and faces 101st-ranked Erika Andreeva in her opening match.
Swiatek and Sabalenka are separated in the two halves of the draw, meaning they could not play until the final on 8 June.
In the second round, Poland’s Swiatek could face four-time major champion Naomi Osaka, who is back at Roland Garros for the first time since returning from maternity leave and starts against Italy’s Lucia Bronzetti.
American third seed Coco Gauff has been drawn in the same half as Swiatek, meaning they could face in the semi-finals.
In the men’s draw, Italian second seed Jannik Sinner plays American Chris Eubanks, while Spanish third seed Carlos Alcaraz takes on a qualifier or lucky loser.