PARIS — Only six years ago, Ana Ivanovic, the 19-year-old from Belgrade, Serbia, who will play for the French Open title on Saturday, was hitting tennis balls inside an empty, Olympic-size swimming pool. The club that owned it didn’t want to spend the money to heat it in the winter, so it drained the water, rolled out some carpet, and set up two nets.

“It was impossible to play crosscourt, because it was this far from the wall,” Ivanovic, squeezing two fingers together, said. “So we had to keep playing down the lines.”

Ivanovic hit plenty of winners down the line yesterday against Maria Sharapova in a 6–2, 6–1 victory. She hit some crosscourt, too, and sprinkled in five aces against only 11 errors. She returned serve as if she were hitting balls out of her hand: a step into the court, a short, crisp stroke, and watch Sharapova run (or groan or look around in disgust). Start to finish, it was the best match of Ivanovic’s young life, and it left her giddy and beaming — a common pose for this striking 6-foot-1 teenager these last two weeks — at her press conference.

“It’s very exciting times for me,” she said. “So it’s a little bit hard to calm down.”

The stories of Serbian players have dominated this tournament. Novak Djokovic, 20, one of the most talented youngsters on the men’s tour, plays Rafael Nadal in the semifinals Friday. Jelena Jankovic, a 21-year-old who practiced in the pool, too, came up short yesterday against two-time defending champion Justine Henin, who will face Ivanovic on Saturday.

While all three of these charming athletes have much in common — hardships, memories of the 1999 NATO bombings, six-hour bus rides to the nearest open airport, in Hungary, as Ivanovic explained yesterday — Ivanovic’s story is unique, and in many ways, the most compelling.

Djokovic and Jankovic both honed their skills at tennis academies away from home: Djokovic in Germany under Niki Pilic, a former Croatian tennis pro, and Jankovic at Nick Bollettieri’s academy in Bradenton, Fla. Ivanovic left Serbia, too, thanks to a man from Tel Aviv who knew nothing about developing tennis stars, but a lot about business.

Dan Holzmann, 36, has made a good living from the vitamin drink Juice Plus. He had resided in Switzerland for about 20 years when his tennis instructor, a man of Serbian descent, told him about Ivanovic. Holzmann was intrigued, and soon Ivanovic, whose sponsor was facing bankruptcy, and her mother flew to Switzerland for a visit.

“It took me two hours,” Holzmann said of his decision to invest in Ivanovic’s future. Money, he said, was never the motive. He liked Ivanovic and her family from the start and wanted to help. He soon settled on a coach, Eric van Harpen, well known in tennis circles for his work with Conchita Martinez, Patty Schnyder, and others. Over the next few years, Holzmann said he spent more than $500,000 on equipment, coaching, and travel expenses for Ivanovic, as well as traveling expenses for her mother.

“I was lucky,” he said. “I know a few managers here who have 20 players, nobody in the top 10. And I picked one — it was like the lottery.”

Ivanovic, the no. 7 player in the world when this tournament began, repaid Holzmann, now her business manager, in less than two years as a professional. He recently negotiated a switch from Nike to adidas, which seems to view Ivanovic as the anti-Sharapova: tall and beautiful, but brunette rather than blond and, gasp, friendly.

Ivanovic doesn’t seem much interested in the business side of her career at this point, at least not to an extent that might distract her, as has happened to other potential top players. Holzmann said that van Harpen deserves the credit for transforming Ivanovic from a talented junior into a professional. Since then, she’s had two coaches, but her current part-time adviser, Sven Groeneveld, an adidas coach who works with players sponsored by the company, said Ivanovic’s motivation — and her need for independence — is such that she hasn’t needed as much guidance as other youngsters.

“Great players have very strong personalities,” Groeneveld said. “They need people more who support them, not tell them what to do. I’m a person who likes to listen more to what they want to do.”

Ivanovic, who reached the quarterfinals of this event two years ago and won a clay-court warm-up event in Berlin, has improved considerably in the last few years, and she’s clear about her goals: She wants to be the no. 1 player in the world. She might have the game for it. Her strokes are compact and powerful, and her simple service motion produces surprising power and spin. Speed and footwork remain her greatest weakness, though she is moving better now that she has lost a little weight, Groeneveld said. She also volleys fairly well, though she doesn’t approach the net too often.

Is she playing well enough to defeat Henin? Ivanovic has played the Belgian on clay before: In their first and only meeting two years ago, in Warsaw, Henin won 6-4, 7-5 in the semifinals. Henin played beautifully yesterday, and she’s shown more emotion — more fist pumps and more shouts of “Allez!” — in her last two matches than she usually does. After reaching the final of all four majors last year and winning just one, she seems primed for a third straight title here, and then a run at her first Wimbledon, the only major she has yet to win.

Ivanovic won’t have any advice from Groeneveld, as his contract doesn’t allow him to help one Adidas player beat another (the company sponsors Henin, too). But this Serb is used to independence, and she should have the devil-may-care attitude of an underdog. If she can keep her excitement in check and find a way to take a lead in the first set, she’ll have a chance. Amazing how her odds have improved since those practice sessions in the pool, six long years ago.

tperrotta@nysun.com