The far-right group, Generation Identitaire (Identity Generation) in April last year staged an operation at an Alpine pass to stop migrants, largely from Africa, entering France from Italy.
Around 100 people dressed in blue overalls, hired two helicopters and even erected a symbolic border.
The three on trial – the group's chief Clement Gandelin, its spokesman Romain Espino and another activist Damien Lefevre – have been charged with seeking to confuse the public that they were members of the security forces.
Prosecutors said on the first day of the trial in the southeastern French town of Gap that the three should be handed jail terms of six months and Generation Identitaire fined €75,000.
Their action had caused a furore in France where, as with many European countries, there has been growing tension over the passage of migrants within the border-free Schengen zone.
Pro-migrant activists had responded to the April action by assisting some 30 migrants to cross the French-Italian border. Seven of these activists were convicted at a trial in Gap in December with two handed prison sentences.