The judge halted the trial for several months because several of the defendants who reside in France were not present, Radio France Internationale said.
The defendants include a man who allegedly posed as an Algerian doctor and ran a clinic where unmarried Algerian women were paid to give up their babies for adoption in France.
RFI said some of the women claimed they were threatened and forced to give up their children.
The trafficking ring was broken up after a woman died while undergoing an abortion in 2009.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Aaron Carter is still in love with Hilary Duff