Simon, the tournament's second-seed, beat Italy's Italian Simone Bolelli 7-6 (7-5), 7-6 (7-5) in a first-round match.
Simon, the No. 13 player in the latest men's world rankings, recorded his 40th match win in 2009 in his effort to earn enough points to qualify for the season-ending men's singles final at the Barclays World Tour event in London next month.
Benneteau, the fifth seed, topped Africa's Kevin Anderson 7-5, 6-2; while Mathieu, the sixth seed and the 2002 Lyon winner, downed Argentina's Leonardo Mayer 7-6 (7-5), 6-2.
Other winners Wednesday were Belgian Olivier Rochus; German Nicolas Kiefer and France's Florent Serra.
Celebrity Families of 2014 [PHOTOS]