Cosette has a father, Félix Tholomyès, a student in Paris. Their love story is told together with three other pairs of lovers. I believe Hugo’s intention was to show that their story represents the working-class people of France at the time. Hugo was very clear about not to put too much emphasis on the identity of Fantine’s lover: 

“These young men were insignificant; everybody has seen the type; the four first comers will serve as examples; neither good nor bad, neither learned nor ignorant, neither talented nor stupid; handsome in that charming April of life we call twenty.” 

On Fantine’s birth, Hugo’s intention is also similar.

“Fantine was one of those beings who are brought forth from the heart of the people, so to speak. Sprung from the most unfathomable depths of social darkness, she bore on her brow the mark of the anonymous. She was born at Montreuil-sur–mer. Who were her parents? Who can say? She had never known either father or mother.”

To make her stand out from the rest of the girls, he did heap many praises on Fantine’s beauty and innocence, and when combined with the later story, gives the feeling that it is a tragedy of a fallen angel.

“An observer who had studied her attentively would have found through all this intoxication of her age, of the season, and of love, an unconquerable expression of reserve and modesty. She remained a bit wide-eyed. This chaste wonder is the nuance that separates Psyche from Venus. “

Fantine’s descent is partly because of the negligence of Tholomyes, partly because of “the itching for scandals” of the small town people (particularly Madame Victurnien, “keeper and guardian of everybody’s virtue”), partly because of the greed and wickedness of Thenardiers. But that’s the plot. What does Hugo want to say using this plot? He wrote:

“What is this story of Fantine about? It is about society buying a slave.
From whom? From misery. 
From hunger, from cold, from loneliness, from desertion, from privation. Melancholy barter. A soul for a piece of bread. Misery makes the offer; society accepts.
The holy law of Jesus Christ governs our civilization, but it does not yet permeate it. They say that slavery has disappeared from European civilization. That is incorrect. It still exists, but now it weighs only on women, and it is called prostitution. 
It weighs on women, that is to say, on grace, frailty, beauty, motherhood. This is not the least among man’s shames. “

I think Hugo had been pretty vague here. He didn’t point fingers. People may mourn her fate without getting angry at any particular person. There might not be any systematic social injustice Fantine’s fate embodies, except, perhaps, prostitution. (In the introduction of the book, Lee Fahnestock, the translator of the book, mentioned that a chapter on prostitution and woman’s lot was cut when the novel was originally published but was recently added as an appendix to some french editions.)  What he might want to say is how society weighs on those who dwell at its bottom.  Her tragedy is completed when she died without saying Cosette again.

If one follows the guideline given by Hugo and think that Les Miserables goes from darkness to light, Fantine’s story only makes sense when it is contrasted with the story of Cosette’s. As Hugo described at the end of the book, when Jean Valjean finally reveals to Cosette, the identity of her mother, he said:

“Cosette, the time has come to tell you the name of your mother. Her name was Fantine. Remember that name: Fantine. Fall on your knees whenever you pronounce it. She suffered a great deal. And loved you very much. Her measure of unhappiness was as full as yours of happiness. Such are the distributions of God.”