I would like to perhaps take this question a bit deeper. No doubt that the previous answer is right in that she does not have a husband. Indeed, she also leaves because of a broken heart. Yet, I think that there is more here with which Flaubert means to leave the reader. On one hand, Felicite is young enough to certainly experience more of a sensuous or carnal nature of love. However, she does not. Once she experiences the inauthentic and self serving nature of love as offered by Theodore, she seems to immediately grasp that her expression of love is something that is "different" than those around her. Part of the reason why Flaubert writes her as never having a husband is because it is at this point that he starts to construct her character as representing a more universal and transcendent notion of love. She does not have a husband because this is something that is specific and of "this world." Yet, Felicite starts to express this transcendent conception of love in her affection for Madame Aubain's children, and from then on, in all of reality. It is for this reason that I would say that her heart is not broken, but rather made aware of the reality that what she possesses in it is something that needs to be shared with as many people as possible. Contrary to other works of the time period and even attitudes that exist today, Felicite is not depicted as less of a person because she lacks a husband and children. Rather, quite the opposite happens. She is presented as a more unifying and coherent force to the malignancy and cruelty of this life because of her capacity to love and to express it in a universally transcendent manner. Due to this overarching expression that brings meaning into a world that lacks it, Felicite's characterization supersedes needing a husband.
No felicite does not have a husband, she left her life as a cow-herder because of a broken heart, which is when she was employed by Madame Aubain.