Estelle Derieux, 34, showed no emotion as the verdict was read out in the court in northern France.
She had previously claimed she killed her daughter in Lille in August 2013 out of fear she was about to be taken away by social services.
A psychologist testified earlier this week that Derieux suffered from bipolar disorder, and was trapped between "angel and demon".
"She has an angelic face, she can smile, but three minutes later, she can become demonic," said the expert.
Derieux told the court during the trial that she "didn't understand that (social services) wanted to help her" and apologised for her actions.
"I am asking myself certain questions. I am trying to change, to be more open to advice, to listen more," she said.
"My girl -- I can't talk about her in the past tense, I always talk about her in the present."
The court also ruled that Derieux should receive psychological treatment.