The fourth-seeded Frenchman beat Australian Bernard Tomic 6-4 7-5 to continue his good form after winning the Moselle Open last time out in Metz.
Simon will meet Holland's Igor Sijsling in the last eight in Friday's opening match.
Third seed Milos Raonic also ousted an Australian as he needed three sets to beat Marinko Matosevic 7-6 (7/3) 4-6 6-4.
Canadian Raonic fired down 21 aces and will face Feliciano Lopez next.
Mikhail Youzhny reached his fifth tour-level quarter-final of the year after a 6-3 6-3 win over Denis Istomin, while Lu Yen-hsun upset eighth seed Lukas Rosol 6-3 6-2.
Second seed Richard Gasquet won through with a comfortable 6-3 6-2 win over Lukas Lacko.