The 22-year-old swept to the Olympic title at Roland Garros last August and her 6-2 6-3 victory over Arango underlined why she is being tipped to win her first Grand Slam.
On cool and drizzly Court Suzanne Lenglen, eighth seed Zheng had too much firepower for her tricky 85th-ranked opponent, breaking serve at will during an impressive performance.
It was not all perfect though, with Zheng dropping serve in the opening game of the match and then twice in succession early in the second set as Arango began to extend the rallies and test the patience of her opponent.
But Zheng, the only Chinese player in the second round, remained focused on reaching round three at the French Open for the third time in four appearances.
"It's not easy to play her, she put every ball back," Zheng, runner-up at the 2024 Australian Open, said on court. "It was not easy to finish the points.
"I was really happy with my performance today."
Next up will be Canada's 18-year-old qualifier Victoria Mboko after the world number 120 continued her impressive debut with a comfortable 6-4, 6-4 win against Germany's Eva Lys.
Mboko is yet to drop a set through three rounds of qualifying and two in the main draw.