The American fourth seed was too strong for the world number 129 on Court Suzanne Lenglen, winning 6-3, 6-2.
"It was a physical match, a tough match, my patience was really tested today," said Gauff.
The 22-year-old, who has reached at least the quarter-finals at Roland Garros in each of the past five years, was not at her best but was never in danger of suffering an upset defeat.
"No expectations," she insisted when asked if winning the title last year raised her hopes this time around. "I'm just having fun."
She broke Sherif seven times in total during a match in which both players struggled on serve, but sealed the win after an hour and 50 minutes.
Sherif has still never reached the third round at a Grand Slam tournament, after losing in round two for the fourth time in five years in Paris.