Williams has won 19 of 21 head-to-head matchups against Sharapova, including the past 18 in a row.
Five-time Grand Slam champion Sharapova, the victor in Paris in 2012 and 2014, hadn't played on Roland Garros' showpiece arena since a quarter-final exit in 2015.
"It's not really important for me to be No. 1 or No. 2 in my country, I know for people it's important, they always ask you 'what do you think about being French No. 1?' but I'm just trying to be the best I can on court and for me the most important is my world ranking, how I play on court, how I improve", she insists.
"I think it's normal". You can't give someone of Serena's caliber that many looks at second serves and put yourself under the pump that much. I was surprised about that, to be honest. Some criticized my decision, but I knew I had two loves-tennis and fashion-and had to find a way to make them coexist.
"I wanted to read the book and I was really excited for it to come out and I was really happy for her".
And, while Sharapova conceded that it would not be easy to beat Williams, the 6ft 2ins superstar promised to fight for her place in the quarter-finals.
Williams had played only four matches since taking time off due to pregnancy before arriving at Roland Garros. Women's third seed Garbine Muguruza dismissed Aussie Samantha Stosur 6-0, 6-2; Estonia's Anett Kontaveit moved past Czech eighth-seed Petra Kvitova 7-6 (6), 7-6 (4); US Open champion Sloane Stephens beat Italy's Camila Giorgi 4-6, 6-1, 8-6.
"I didn't request it because it's a big court, but Philippe Chatrier is different from all the other courts, it's huge on the side so it's changing all the perception you have".
She claimed an important victory against Cornet on that stadium en route to the quarter-finals a year ago.
"I remember one day, I couldn't find Olympia's bottle and I got so upset I started crying ... because I wanted to be ideal for her".
The win sets up a potential thriller against Sharapova, who saw off Karolina Plisokova in straight sets earlier on Saturday. Until Sharapova can be trustworthy with her serve, she's going to have a hard time against top tier players. "You know the challenge that is upon you", Sharapova said.
But for all the bad blood between the two over the years - often involving claims and counter-claims over their private lives - Sharapova added in her book that reconciliation may come once the on-court battles are over.
'Not long after the tournament, I heard Serena told a friend - who then told me - "I will never lose to that little b**** again"'. I think, to some extent, we have driven each other.
After winning the 2017 Australian Open while secretly pregnant, Serena took the rest of the season off and welcomed her baby girl with now-husband Alexis Ohanian on September 1.