The 26th-ranked Cornet scored her first career victory over a No. 1 player when she upset Serena Williams 6-4, 6-4.
"I'm so excited," Cornet said, smiling broadly. "I didn't expect that definitely, and I'm really, really happy and proud of myself.
"She's one — or maybe — 'the' biggest champion of history, and, wow, just thinking that I beat her today."
Earlier in the day, Venus Williams earned her spot in the final when she dominated eighth-seeded Caroline Wozniacki of Denmark 6-3, 6-2.
Serena Williams, playing in her first tournament since losing in the Australian Open fourth round, offered no excuses. She said her back, which had been hurting in recent weeks, was fine.
"I'm a wee bit embarrassed," said Williams, who started laughing. "She played really well. I just didn't play today.
"I tried, though. I don't think I have made that many errors in a match in I think at least three years, maybe four years."
Williams gave herself a failing grade for being unable to find a winning formula for the match: "I think out of a 10, I was at like a negative 283."
Cornet won the first set when Williams flinched while serving in the ninth game.
Cornet, who reached the Paris Indoors semifinal earlier this month, took advantage of her one-set point in the 10th game with a winning backhand down the line.
The Frenchwoman then jumped out to a quick 2-0 lead in the second set, but Williams rebounded.
Cornet broke Williams' serve again in the seventh game with a winning forehand down the line.
Williams fought off four match points on her own serve in the ninth game, but Cornet served out the match at love.
"I know her, and I know she feels the moment when she has to put more into making the opponent feel that she's still here," Cornet said. "But I did it, too. I showed her that I would be there till the end.
"So when she was screaming louder, I was screaming louder. She was hitting harder, I was hitting harder."
In contrast to her sister, the 44th-ranked Venus Williams has been playing top level tennis all week long in Dubai.
A former two-time Dubai champion in 2009 and 2010, Williams currently holds a 14-match winning streak at the tournament. She didn't play in this event between 2011 and 2013.
"I feel like I've just gotten so much better since my first round to now, just feeling comfortable on the court, feeling comfortable when I'm behind, feeling comfortable when I'm in the lead," Williams said.
Williams, who lost the Auckland final to Ana Ivanovic last month, lost an early 2-0 lead in the first set. But from 2-2, Williams always held the lead in the match.
Williams failed to serve out the first set at 5-2, surrendering that eighth game at love. Wozniacki, however, surrendered her serve — and the first set — on a second set point in the next game
Williams broke Wozniacki's serve at 15-40 with a textbook backhand volley for a 2-0 lead in the second set. She broke serve again in the eighth game for the win.
"I didn't really feel like I could go out and play what I wanted to play," said Wozniacki, who won the Dubai trophy in 2011. "Once I got going, she started to play better as well. It was kind of uphill today."
Venus Williams holds a 3-0 lead in matches played against Cornet.