The assaults by the 48-year-old man, named in the French media as Andrew Geddes, allegedly continued for a period of six years.
Geddes, originally from New Jersey, has admitted to raping one girl but says the sex with the others was consensual, prosecutor Robert Gelli said on Wednesday.
The coach is accused of repeatedly raping and sexually assaulting his then 12-year-old student between 1999 and 2001.
He is also suspected of the same crimes against two girls who were under 18 between 2001 and 2005.
The prosecutor said the suspect had also beaten the girls and had filmed one of them while he forced her to give him oral sex.
The alleged assaults took place at Sarcelles tennis club near Paris and during tennis tournaments in other locations near the capital and on France’s Atlantic coast.
The American subsequently went to work for Levallois Sporting Club in a posh Paris suburb.
Levallois Sporting Club issued a statement on Wednesday saying that the crimes allegedly committed by the American coach were prior to his arrival at the club in 2008.
It said his work at the club had been entrely satisfactory and that there had never been any complaints about him either by students or their parents.
The statement added that when it hired the coach, it had no information about what he might have done at the Sarcelles club.
Henri Leconte, the French former tennis champion who is now president of the tennis section of that club, said he had immediately suspended the coach when he heard of the allegations against him.
“This is a situation that has arisen yet again in the sport,” he told RTL radio. “These are people who are sick, who need treatment.”
In February, a French court upheld a rape conviction against a former top tennis coach and added two years to his sentence, making a total of 10 years behind bars.
Régis de Camaret had been convicted in 2012 of raping two under-age girls at the tennis training camp he ran at the plush Mediterranean resort of Saint Tropez in the 1980s and early 1990s.
Camaret, now in his early seventies, counted former Wimbledon runner-up Nathalie Tauziat and former French national champion Isabelle Demongeot among his pupils.
Demongeot was among those who filed complaints against Camaret.
She told the lower court she had been raped for nine years between 1980 and 1989, beginning when she was in her early teens.
by Rory Mulholland