The parents had initially said that the child, named Maëlyne, had fallen unconscious after she drank a glass of rosé wine left by a guest at their house in Champagné, west of Paris.
Maëlyne was in a coma when she was rushed to a hospital in nearby Le Mans. Doctors could not save her and she died on the night of 27 February 2015.
Doctors quickly dismissed the claim that the girl had drunk wine after they found in her body toxic doses of drugs usually prescribed for adults suffering from depression.
Investigators later found traces of the same drugs in the bottle of the couple’s other daughter, who was three at the time of Maëlyne’s death.
Police suspect that the parents, Delphine Niepceron, 27, and Cyrille Le Got, 43, administered the drugs to stop their children crying and to get them off to sleep.
The couple, who deny any wrongdoing, went on trial in Le Mans on Monday charged with administering dangerous substances that led a person’s death, but without the intention of killing that person.