Sixth seed Williams, who turned 39 on Saturday, overcame a rusty start to beat her fellow American 7-6 (7-3) 6-0.
Once she came through a 74-minute opener, Williams began to play with more belief and clarity as she swept Ahn aside in a 27-minute second set.
Williams will play Bulgaria’s Tsvetana Pironkova in the second round in Paris.
Pironkova, 33, was handed a wildcard by Roland Garros organisers after a memorable run to the US Open quarter-finals – where she lost to Williams – in her first tournament since 2017 after giving birth.
Pironkova set up the rematch with a 6-3 6-3 win over Germany’s Andrea Petkovic.it comes to trying to land another Grand Slam title.
One more major triumph would allow her to equal Australian Margaret Court’s long-standing record and become the fourth mother to win a Grand Slam singles title.
The passion of the American is undiminished, saying in the build-up that she would not play on the clay courts in Paris if she did not believe she could win.
Going out in the semi-finals at the US Open was – by her standards – regarded as a disappointment and even though she is not considered one of the favourites on her least comfortable surface, anything other than victory at Roland Garros will also be viewed by many.