In Madame Bovary, both Rodolphe and Charles blame fate for the outcomes of their respective relationships with Emma. The validity of their arguments is debatable.
Fate is a term used to describe an inevitable, predetermined thing or event that is beyond one's control. It can certainly be argued that fate plays a role in Emma's downfall, but there are other contributing factors.
Emma is born into the middle class but has upper-class taste. Her social status is a matter of fate: she cannot help that she is not born into wealth. However, Emma's reactions to the misalignment between the life she desires and her reality are largely matters of choice rather than fate.
Emma marries Charles of her own volition. When her marriage fails to bring her the happiness she expects, she chooses to cope with her pain and disappointment by living beyond her means. She chooses to borrow more money than she can afford to pay back, resulting in the accumulation of a large debt to Lheureux. She chooses to have extramarital romantic relationships, which bring her fleeting happiness but ultimately cause her more heartache.
Emma relies too heavily on others for her own happiness. She puts her happiness in the hands of men who always end up hurting and disappointing her. This is not entirely her fault, but she is somewhat to blame because she chooses to be with these men.
When she finds herself rejected by her lovers and in severe debt, Emma once again makes a choice and decides to commit suicide. While fate does play a limited role in her social station and undoing, most of Emma's downfall results from her own poor choices.