Veronique Courjault, 41, had been accused of killing them and then burning one of the bodies and stashing two others in a freezer. The case was followed closely in France since police launched their investigation in 2006.
In France, murder charges carry a maximum penalty of life in prison. But the prosecutor in the case on Wednesday had recommended Courjault be given a 10-year prison sentence.
Courjault will only serve around five years of the eight-year sentence because she had been in custody during the investigation.
During the trial, in the western city of Tours, psychiatrists testified that she suffered from a psychological condition known as "pregnancy denial," and family members pleaded for clemency on her behalf.
Her husband, Jean-Louis Courjault, praised the relatively light sentence, which he said "will allow us to rebuild, to make out the light at the end of the tunnel."
It was Jean-Louis Courjault who discovered the bodies of two of the babies in a freezer in July 2006 and alerted authorities in South Korea, where the couple lived at the time.
The couple initially denied the babies were theirs, but Veronique Courjault later acknowledged having given birth to them in 2002 and 2003. She also confessed to killing a third baby, born in secret in France in 1999, and burning its body in a fireplace.
In emotional testimony Wednesday, Courjault confessed to the triple infanticide.
"I killed my children," she said between sobs. She added that "absurd" as it may sound, "I was conscious of being pregnant, but not of being pregnant with babies."
She said she did not consciously set out to hide the pregnancies. "It was my body that blocked" the pregnancies, she said. "No relationship with the babies developed."
Jean-Louis Courjault, who has supported his wife throughout the investigation and trial, told the court he believed his wife has "big problems."
"It's clear that Veronique's actions were absolutely not calculated. For me, she's ill," he said. He pleaded for clemency on his wife's behalf and that of the couple's two adolescent children.