She also knew, of course, what happened a year ago in Paris: the only first-round Grand Slam loss of her career, to a woman ranked outside the top 100, no less.
Eager to repeat the elation of 2002, and motivated by the disappointment of 2012, Williams used terrific defense and her usual powerful hitting in Saturday's final, closing with a crescendo of aces -- three in the last game -- for a 6-4, 6-4 victory over defending champion Maria Sharapova to collect a second Roland Garros title and 16th major trophy overall.
"I'm still a little bit upset about that loss last year," the No. 1-ranked Williams said with a chuckle, her shiny new hardware an arm's length away.
"But it's all about, for me, how you recover," she continued. "I think I've always said a champion isn't about how much they win, but it's about how they recover from their downs, whether it's an injury or whether it's a loss."
As she spoke those last few words, her voice choked and her eyes welled with tears. There have been low moments for the 31-year-old American -- none worse, perhaps, than a 10-month stretch ending in 2011 that included two foot operations and treatment for blood clots in her lungs -- but she's enjoying a high point right now.
Saturday's victory was her 31st in a row, the longest single-season streak in 13 years. Williams is 43-2 with six titles this season.
"She is playing extremely well," Sharapova said. "She's a competitor."
Sharapova is known for her grit on a court, too. She entered Saturday ranked No. 2, the winner of her last 13 French Open matches, and the only active woman other than the Williams sisters with more than two Grand Slam titles. But she doesn't seem to stand a chance against Serena, who has won their last 13 encounters.
This was the first major final between women ranked 1-2 in more than nine years -- the first at Roland Garros in 18 -- and yet it really was not all that close. Particularly at crunch time.
Under a cloudy sky, and amid a breeze that blew dust in both players' eyes, Sharapova began well enough, saving four break points in the first game, then breaking in the second, prompting plenty of murmuring in the stands.
The next game went to 40-15 on Sharapova's serve, one point from a 3-0 lead. That's when Williams got going. A 13-stroke exchange culminated with a forehand that forced Sharapova's backhand error and started a four-point, break-earning run for Williams. She got to 2-1 with an overhead smash she punctuated with a staredown, a raised left fist and a loud "Come on!"
That fist was aloft again a half-hour later, when Williams' cross-court forehand winner helped her break to lead 5-4, and she served out the set.
Sharapova saved five break points in the second set's opening game, but that merely delayed what everyone expected. Williams got the last break she would need two games later, and it was made possible by the sort of baseline scrambling she did all day. Sharapova struck a forehand down the line that would have ended the point against most opponents, but Williams got the ball back, and with an extra shot necessary, the Russian slapped a forehand into the net.
On break point, Sharapova smacked a 109 mph serve, but Williams' strong return forced another mistake. Now Williams merely needed to hold serve the rest of the way, and half of her 10 aces came in her last two service games.
Sharapova observed that Williams serves "harder than David Ferrer," referring to the man who will face seven-time champion Rafael Nadal in the men's final Sunday.
Serving at 5-4, Williams recalled, "I was just so nervous. I thought, `I'm not going to be able to hit groundstrokes.' No joke. The one groundstroke I did hit went, like, 100 feet out. I thought to myself, `Look, Serena, you've just got to hit aces. That's your only choice."'
Simple as that, huh? Well, with her, yes.
She started with an ace at 118 mph. After a wild backhand miss -- not 100 feet out, but maybe 10 -- she hit an ace at 121 mph. She got to 40-15 with a backhand winner and crouched down, hand to her face, aware she was one point away.
One more strong swing delivered the fastest ace yet, 123 mph. Williams flung her racket and dropped to her knees.
A few minutes later, Williams was addressing an appreciative crowd in French, telling them about her "incroyable" victory and noting she considers herself a Parisian. She owns an apartment in the city and has been working with French coach Patrick Mouratoglou.
"She feels a bit at home here," Mouratoglou said.
Williams hadn't been back to the final in Paris since beating her sister for the 2002 title. From 2003-11, she lost in the semifinals once, the quarterfinals four times, the third round once, and missed the tournament three times because of injury. Then came last year: Williams was 17-0 on clay when she arrived in France, then quickly 17-1.
"She was so devastated by that," said her mother, Oracene Price.
Soon after, Williams began practicing at Mouratoglou's tennis academy. And however demoralizing that loss was, it turned out to be career-rejuvenating. Since then, Williams is 74-3 and has won three of the last four Grand Slam tournaments.
She is the oldest woman to win the French Open in at least 45 years, and the oldest at any Grand Slam since Martina Navratilova was 33 at Wimbledon in 1990.
"I really believe age is a number at this point, because I have never felt so fit. I feel great. I look great," she said, laughing at her own joke. "If I see someone that's 31, I'm like, `You're old.' Then I'm like, `I'm 31.' But I don't feel it at all."
At the moment, no current players can keep up with her.
If she keeps playing like this -- if she maintains her focus and, most importantly, stays healthy -- the real challenge is how she will stack up with past greats of the game.
"I feel like I definitely want to continue my journey," Williams said. "If it means I stop at 16 or if it means I have more, I definitely want to continue my journey to get a few more."
She's won the sixth-most major titles in the history of tennis, which dates to the 1880s. Add two more, and she'll equal Martina Navratilova and Chris Evert with 18. Would anyone be surprised if Williams got there by the end of this year?
The only women with more are Margaret Smith Court (24), Steffi Graf (22) and Helen Wills Moody (19).
"For Serena, nothing is out of reach," Mouratoglou said. "If she really wants something, it's very difficult to stop her."
Shortly after Saturday's match ended, Williams found Mouratoglou near the players' lounge and wrapped both of her arms around his neck for a long embrace. Then they headed down the stairs leading to the locker room. Williams told Mouratoglou she wanted to go do some cool-down exercises to stretch her back.
Wimbledon begins two weeks from Monday. There are more matches to win, more trophies to collect, more history to be made.
"I want to go out in my peak. That's my goal," Williams said. "But have I peaked yet?"
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