The case in 2009 fined two branches of the group's French operations, the so-called Celebrity Centre and the SEL bookshop, and several of its leaders.
Fines of €600,000 ($824,000) were levied after the court heard complaints from two women, one of whom said she was pressured into paying more than €20,000 for questionable remedies in the 1990s.
The head of Scientology in France, Alain Rosenberg, was given a two-year suspended jail sentence and a €30,000 fine. Four other leaders were also fined.
A 1995 parliamentary report classed Scientology as a sect in France, rather than a religion, and prosecutors had originally hoped the case would result in its operations being closed down. However, judges stopped short of imposing a ban due to a law passed earlier that year banning the dissolution of an organization for fraud.
At the time of the original judgement, Scientologists said they would appeal.
"Religious freedom is in danger in this country," said Eric Roux, a spokesman for the Celebrity Centre.
According to Le Monde newspaper, lawyers will demand the "cancellation of the October 27th 2009 judgement" and will raise "one or several questions of constitutionality."
The church of Scientology was founded in 1954 by the science fiction write L Ron Hubbard and followers include stars such as Tom Cruise and John Travolta.
There are 12 million Scientologists worldwide, including an estimated 45,000 in France.