The plaintiffs' lawyers argue that Scientology resorts to harassment and pressure to recruit victims who show signs of vulnerability.
The church's French branch has said the case could threaten freedom of religion in the country.
'Psychological holds exerted'
Daniele Gounord, the group's spokeswoman in France, rejected the accusations and said Scientologists were facing persecution.
"This is a trial for heresy," she said, adding that the church was being "hounded" in French courts because it advocates new ideas.
The Paris Scientology Celebrity Centre and six of its members are also on trial, accused of preying on vulnerable followers "with the goal of seizing their fortune by exerting a psychological hold".
Some members also face charges of illegally supplying pharmaceutical products, after complainants said they were given remedies to improve their mental state.
Seven church officials were initially charged, but one has since died.
If convicted, they face a maximum sentence of seven years in jail and fines.
Scientology, founded in the US in 1954 by science fiction writer L Ron Hubbard, was officially recognised as a religion there nearly 20 years later.
It is known for its Hollywood celebrity followers including actors Tom Cruise and John Travolta.
In Europe, the church is often accused of exploiting its members financially.
The church has faced court a number of times in France, with members convicted of fraud in Lyon in 1997 and Marseilles two years later.
In 2002, a court fined it for violating privacy laws and said it could be dissolved if involved in similar cases.
The latest trial is scheduled to continue until June 17. A ruling is expected at a later date.
Even if the court rules in favour of the plaintiffs and decides to impose a ban, the Church of Scientology has the right to appeal and legal wrangling could continue for years.