The 24-year-old, who had never previously beaten any top-20 player, recorded a 1-6 6-3 6-4 triumph earlier today to inflict Williams's earliest defeat in the competition since 2005.
"I just cannot believe it," Cornet told BBC Sport. "Three years ago I couldn't play on grass, I was so bad, but now I have beaten Serena, the world number one on her own court.
"I have to get used to it and focus on the next match because the tournament is not over for me. I am not sure how I did it but just with the heart and the help from the crowd."
Cornet will face Canada's Eugenie Bouchard in the next round for a place in the quarter-finals.