The girls’ families say that both has been treated in the same incubator when they were born but a nurse mixed-up the babies when handing them back to their parents upon being discharged.
Although the error was discovered 10 years ago, neither family has wanted to swap the girls back.
On Tuesday, the court in Grasse ordered the clinic in Cannes to pay €400,000 to each of the girls.
Their parents were awarded €300,000 and the clinic must pay €60,000 each to three siblings.
One of the mothers, Ms Sophie Serrano suspected the switch when her daughter, born in 1994, was handed back to her after being treated for jaundice, with the difference in skin tone and hair length of the baby.
But the clinic’s admin dismissed her suspicions and they brought the child home.
Ten years later, still plagued by doubts, Ms Serrano and her husband had tests which proved neither of them was the biological parent of their daughter, Manon.
After an investigation, the two families made contact with each other and eventually took the case to court, but there was never any question of reversing the swap.
The two families have since then distanced themselves from each other.
Manon Serrano described meeting the other family as “a pretty disturbing moment”.
“You find yourself in front of a woman who is biologically your mother but who is a stranger,” she said.