Cold as Summer (2002)

Rachel is a young woman with a little daughter, but it seems that she can't make an emotional connection to her or care for her. She would very much like to live her life and have fun, but the child presents a millstone around her neck. So she often drops the infant at her neighbor to baby-sit and goes out. One day she decides to leave for good, heading to the Côte d'Azur, and leaves her neighbor a note to look after her child - not knowing that she's on vacation. The child dies, and of all people a middle-aged married female detective who is desperately trying to get pregnant is assigned the investigation.