In the first meeting between the two players, it was the home hopeful who had the better of the early exchanges, but he was unable to turn a tight game in the third to his advantage.
The set went with serve until Anderson broke for 4-2, before wrapping it up with another break and his first set point of the contest.
In the second Anderson continued his dominant play with a third break in a row to go 3-0 ahead. He was broken back for 3-2, but a key break in the very next game saw the South African see out the set comfortably.
By now the Frenchman was really struggling to hold serve and he was broken three times on the way to defeat in the final set, which saw Anderson into the third round.