Cornet beat Hsieh Su-wei 6-4, 6-4 and Simon, who moved up in the rankings from No. 29 to 7 last year, defeated Lu Yen-hsun 6-3, 7-6 (8) to give France a 2-0 winning lead after the two singles matches.
Cornet and Simon beat Hsieh and Lu 6-4, 7-6 (9) in mixed doubles to complete a 3-0 win, saving five set points in the tiebreaker. The French duo next play Italy on Tuesday.
Simon had problems closing out the Taiwanese player in the second set, allowing Lu to break his service in the sixth game to get back into the match and force a tiebreaker.
"I played great tennis and then when I was 6-3, 3-1 up I just lost my concentration and he played better,'' Simon said. "I'm a little bit lucky because I should have lost the second set.''
Both Cornet and Hsieh had problems with their serves in the opening set, and Hsieh was 0-for-4 in her breakpoint chances. Cornet succeeded once in five tries - in the ninth game when she took a 5-4 lead - then held serve and won the set with an ace.
Before the second set started, Hsieh has a medical time out to receive treatment for a stiff neck, and the physiotherapist was back several times between games to give the Taiwanese player additional treatment.
"It's something like 3 a.m. in France right now, so I was not in the best of shape,'' Cornet said. "I felt out of breath at times, but it's nice to get the win.''
It was the only Saturday match at the mixed teams event. On Sunday, Russia, featuring the brother-sister combination of Marat Safin and Dinara Safina, plays Italy's Flavia Pennetta and Simone Bolelli.
Lleyton Hewitt, who hasn't played since the Beijing Olympics due to a hip injury and subsequent surgery, partners Casey Dellacqua when Australia takes on Germany in one of two matches Monday.
The defending champion United States, represented by Meghann Shaughnessy and James Blake, takes on Slovakia in the other Monday match.
The U.S, Australia, Germany and Slovakia are playing in Group A while Russia, France, Italy and Taiwan are in Group B. The winners of each group play in the final next Friday.
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