PARIS - What was Sloane Stephens saying to herself as she kept piling up points and games today out on Court 5 against fellow American Bethanie Mattek-Sands? It was a big moment for the 19-year-old Floridian; she had a chance to reach the third round of what she calls her favorite tournament for the first time. Was Stephens, who is also vying for a place on the U.S. Olympic team, telling herself to stay calm, stay focused, stick to the plan?

“Yeah,” Stephens said after she had wrapped up an easy 6-1, 6-1 win. “But there’s always more.”

More going on in your head? Such as?

Such as this thought:

“Because my mom is spoiled rotten, she’s going to want to try to fly first class home or something, so I got to keep winning.”

There is always something more with Stephens, who likes to talk and is good at it. And you get the feeling that, after some time spent learning the WTA ropes, there’s going to be more from her as a player. Stephens reached the third round at the U.S. Open last year, and is at a career-high ranking of No. 70 as of this week.

Admittedly, Stephens didn’t have to do too much against a wildly erratic Mattek-Sands, who was off from the start and kept going for, and missing, big shots throughout. But you could see that Stephens, who trains for this event in Spain and says clay is her favorite surface (Why? “I really don’t know”), can play on the foreign red stuff. She’s a smooth mover who covers the corners well. She wins free points with her serve. And she can change pace mid-rally, juicing up her backhand down the line or running around to finish points with inside-out forehands. Stephens also has a unique and deceptive style—it can appear lackadaisical, but it isn’t. She stands mostly straight up and down, keeps her footwork rhythmic rather than hyper, and whips over top of her two-handed backhand. Today Stephens kept the ball deep and let Mattek-Sands hit herself out of the match.

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Stephens, who beat a quality opponent in Ekaterina Makarova in the first round, is nothing if not confident about her chances here. “In 10 years," she said with a smile on Monday, "I better have won this one time at least, otherwise I'll be one unhappy camper.” (Unfortunately, this also led her to darker thoughts about the future: “In 10 years I’m going to be 29. Oh my God!”) For now, one more win will put her a step closer to another dream, a trip to the Olympics. Her next opponent, Mathilde Johansson of Sweden, currently ranked 93rd, is certainly beatable.

Win or lose, though, Stephens will still be living the dream. She says she just keeps trying to have fun, and the irrepressibly fast-talking way that she says it lets you know that she's enjoying the tennis life at the moment. When Stephens was asked what it means for her to be in the third round, she didn’t hesitate to flash a smile and a superlative:

“It’s awesome,” she said.

*****

Fifteen years ago, another young Florida-based African-American woman came to Paris talking about future titles, and relishing a chance to slide on exotic red clay. That player was Venus Williams, and it was hard not to see the parallels between Williams and Stephens today. Even the Paris weather could have been a metaphor for their current situations. Stephens played in the early afternoon sun and won easily. By the time Williams took the court for her second-round match against Agnieszka Radwanska, clouds had rolled in, the temperature had dropped, and rain was threatening. One night after her sister had helped set Chatrier on fire, Venus walked out to a half-filled, mostly dead arena.

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It was clear during the first changeover that Venus’s mood was just as melancholy. Between games, she leaned back, not touching her racquet, and closed her eyes in stone-faced resignation. Venus was a step—or two, or three, or four—slow from the start. She struggled, and often failed, just to catch up to Radwanska’s returns of serve, and Aga is hardly the biggest hitter on tour. The first set was over in 28 minutes, and Venus’s best moment was a stare that she flashed at Radwanska after the Pole passed her with a sharp running forehand. Aga was very good from start to finish. In the second set, she came up with a scrambling lob winner from the front of the court, and lofted another from the baseline to reach match point. She’ll play Svetlana Kuznetsova next, and perhaps Ana Ivanovic after that.

Venus signed autographs when it was over, prompting some to speculate that, 15 years after her celebrated debut here, we might not see her on this court again. But Williams said later, in a press conference that was strangely melancholy and upbeat at the same time—you might say Venus was laughing to keep from crying—that she’ll be back in Paris next year, and that this was all just “the start of a process” of learning to play with the auto-immune disease she has. Some days are better than others, she says, and she never knows how they’ll turn out when she wakes up in the morning.

“I don’t have the magic answer,” she said with a smile. “If I did, you know, I’d be in the third round.”

“I’m still playing a professional sport,” Venus continued philosophically, “so I have to be positive. I’m gonna have ups and downs. [But] I haven’t gotten to the ‘Why me?’ yet. I hope I never get to the ‘Why me?’ I’m not allowed to feel sorry for myself.”

That’s Venus, the strong sister, head always up. Right not she’s finding the bright side in her Olympic hopes. She talked today about her love of the Games, how her father inspired her to aim for them, and how, “When I leave the Olympics, I go through withdrawal.” She said that’s why she was here playing today.

At the moment, Venus has a singles spot on the team by ranking, but she talked tonight about just playing doubles and mixed doubles—it’s all up in the air. Two players would need to pass Venus, who is ranked 57th, to keep her out of the team's four singles spots. One of those players is currently ranked 13 places below her, and is in the third round at Roland Garros. Her name is Sloane Stephens.