28-year-old Griekspoor and 31-year-old Giron have met three times before. Griekspoor won the earliest meetings in Montpellier and Rome, but Giron was last victorious in Vienna in 2022.
Griekspoor, the 35th-ranked ATP player, played his best French Open in 2023, when he reached the third round and eventually lost to Alexander Zverev after a tiebreak in the fifth set. Giron was eliminated in the first round of last year's Grand Slam in Paris.
With a win, Tallon Griekspoor will face either Francisco Cerundolo or Gabriel Diallo in the following round.
Elsewhere in the men's singles draw, Botic van de Zandschulp drew Argentinian Emilio Nava, the 138th-ranked player in the world. Jesper de Jong, who recently entered the top 100, drew 140th-ranked Italian Francesco Passaro, who debuted at a Grand Slam earlier this year in Australia, where he reached the second round of the Australian Open.
The winner between Van de Zandschulp and Nava will meet either Rodrigo Bautista Agut or Holger Rune in the second round. De Jong or Passaro will face the matchup winner between Alexander Zverev and Learner Tien.
Check out the full men's singles draw on Flashscore.
Women's draw
In the women's singles draw, Suzan Lamens, who overtook Arantxa Rus as the highest-ranked Dutch female tennis player, has drawn American Ashlyn Krueger in the first round of the French Open. 21-year-old Krueger, the 37th-ranked player in the WTA rankings, will feature in her second French Open after last year's first-round elimination.
The winner will meet either teenage superstar Mirra Andreeva or Cristina Bucsa in the second round.
Arantxa Rus will face off against Camila Osorio, the Colombian 55th-ranked player in the WTA rankings. It will be the fourth French Open for the 23-year-old South American, who will face Rus in her 11th outing in Paris. The winner of this matchup will face the winner of the match between Clara Tauson and Magda Linette.