This year's event was expected to be the 14-time champion's farewell to Roland Garros, but he has since insisted he could not confirm "100 percent" it would be his last appearance.
Nadal has only played four tournaments since January 2023 after suffering a hip injury and then a muscle tear.
That left him unseeded for the draw and vulnerable to a difficult opening round at a tournament where he has only lost three of his 115 matches.
World number four Zverev arrives in Paris as one of the favourites for the title after winning the Rome Open earlier this month.
"Of course on paper it is not the best draw," Nadal said ahead of the match on Court Philippe Chatrier.
"I play against one of the toughest opponents possible, and at the same time, he came here winning the last event and it's a Masters 1000.
"It's not a small one. So what can I do? That's the draw. Just try to be ready for it."
Nadal, who turns 38 in a week's time, has shown flashes of his best form in the clay-court swing, but was thrashed 6-1, 6-3 by Poland's Hubert Hurkacz in the second round of his last outing in Rome.
He boasts a 7-3 winning record over Zverev ahead of their first meeting since the 2022 French Open semi-finals, when the German left the court in a wheelchair near the end of the second set after injuring his ankle.
"I am not anxious. No, I am focused on trying to play well. That's it," said Nadal.
"Maybe I go there and I repeat the disaster of Rome. It's a possibility, of course. I don't want to hide that.
"But in my mind, is do something different and play much better and give myself a chance to play competitive."
'Didn't want' to play Nadal
Zverev did not play again in 2022 after that ankle injury but has climbed the rankings again in recent months.
The 27-year-old has long been touted as a future Grand Slam champion but remains without one of tennis' four biggest titles.
Clay is his strongest surface, though, and he has reached the semi-finals in each of the last three years at Roland Garros.
The men's draw looks far more open than usual, with doubts surrounding Nadal's fitness and Novak Djokovic having endured a turbulent start to the year.
"I can guarantee you Novak didn't want to play Rafa in the first round and (Carlos) Alcaraz didn't want to play, Jannik (Sinner) didn't want to play him," admitted Zverev.
"I don't want to play him in the first round, but it is how it is. He has been out injured. He hasn't played a lot of tennis. His ranking is where it is. Of course it's not ideal, but at the same time, you know, there is nothing you can do.
"Everybody now is excited for a tough battle and tough first round. I think he's excited and I'm excited for it."
French Open organisers were prepared to stage a tribute ceremony to Nadal to honour his career but the Spaniard was reluctant to endorse such a celebration.
"We were ready to press the button on it," admitted tournament director Amelie Mauresmo.
"But it's Rafa who manages his timing, we follow what he wants. We wouldn't want to put him in an uncomfortable position."
Also on Monday, women's world number one Iga Swiatek starts her bid for a fourth French Open crown against home player Leolia Jeanjean.
Victory for the top seed will give her a second round clash with fellow four-time Grand Slam title winner Naomi Osaka.
Men's Australian Open champion Jannik Sinner, former Roland Garros runner-up Stefanos Tsitsipas and women's US Open title-holder Coco Gauff all get their campaigns underway on Court Suzanne Lenglen.
