The 29-year-old beat Spain's Jaume Munar 6-3, 6-3, 2-6, 6-3 in their first-round men's singles match at the Grand Slam event in the French capital on Monday.
Hurkacz, currently ranked No. 99 in the world, will next face American world No. 22 Frances Tiafoe for a place in the third round.
Meanwhile, fellow Polish player Kamil Majchrzak crashed out of the tournament after a 1-6, 3-6, 4-6 loss to Chile's Alejandro Tabilo in the first round on Tuesday.
On the women's side, Poland's world No. 3 Iga Świątek, along with Magda Linette, Magdalena Fręch and Maja Chwalińska, have all advanced to the second round.
Świątek won the French Open in 2020, 2022, 2023 and 2024.
The 2026 French Open began on Sunday and runs until June 9.
(gs)
Source: PAP