The American, a Roland Garros runner-up in 2022, wrapped up a 6-2, 6-4 success after only 75 minutes on Court Suzanne Lenglen.
Gauff, who has made at least the quarter-finals in each of the past four years, was the beneficiary of 33 unforced errors from her 18-year-old opponent.
She will take on another Czech in world number 47 Marie Bouzkova, in the last 32.
Gauff struggled on serve throughout, being broken five times.
But the only hold of the second set, in the fifth game, proved crucial as she closed out the victory.
"Overall, it was fine. I could have been more aggressive on serve, but the return game was good," Gauff said.
Valentova won both the 2024 girls' singles and doubles tournaments.
The 21-year-old Gauff is bidding for a first title since last year's WTA Finals, after losing the Madrid and Rome finals to Aryna Sabalenka and Jasmine Paolini, respectively.