Firelight (1997) on Netflix

In 1838, lovely governess Elisabeth agrees to bear a child of anonymous English landowner, and he will in return pay her father's debt. At birth she, as agreed, gives up the child. Seven years later she is hired as governess to a girl on a remote Sussex estate. The father of the girl, Charles Godwin, turns out to be that anonymous landowner. So Elisabeth has to be her own daughter's governess, and she can't reveal the secret of her tie with little Louisa.