The advent of dating websites for married people who fancy an affair seemed unlikely to raise eyebrows among the French, long reputed to turn a blind eye to extramarital affairs.
However, French Catholic groups are suing the Gleeden website for openly encouraging people to break their marriage vows.
Catholic family associations last month succeeded in persuading several local councils around Paris to order the removal of advertising posters promoting the joys of adultery after 23,000 people signed a petition against them.
They are now taking Gleeden, founded by two Frenchmen based in New York, to court in France, where the site counts more than a million members.
Adultery has not been illegal in France since 1975, although it still constitutes grounds for a "fault divorce".
But Catholic groups argue that advertising a website promoting extramarital liaisons amounts to "the public promotion of duplicity, lies and breaches of the law".
Their lawyer, Henri de Beauregard, said it was an "encouragement to break a contractual obligation entered into at the time of marriage."
"We have entered an era in which nothing is serious any more," said Jean-Marie Andres, the head of the family groups, whose members helped to organise mass protests against the legalisation of gay marriage in 2013.
"We wanted to get people to think: is adultery something completely negligible, to the point where you can advertise for it?" Mr Andres said. "The dramatic social consequences for families caused by infidelity and the breakdown in the structure of society fuelled by it are not matters that escape the common conscience."
A Gleeden spokeswoman said the lawsuit was "incomprehensible" because all the company's advertising material was "submitted to and cleared by the advertising regulatory bodies".
A previous challenge was thrown out by advertising regulators, but this is the first time Catholic groups are going to court.
The Paris Métro authorities have refused to take down huge posters in the tube, and several Catholic militants who defaced or tore them down were fined €60 each last year.