How does Fantine's lack of education contribute to her problems and ultimate death?
By being uneducated, Fantine is naive. There is much she does not understand about the business world, and she is often confused by the intellectual jesting speech of people around her. She confusing jokes with sincere emotions, which leads her into her catastrophic relationship with Tholomyes. She trusts him, she trusts the Thenardiers, she trusts the integrity of her co-workers, and in all of that she is disastrously mistaken.
Furthermore, her inability to secure better employment because she lacks the skills attending an educated citizen is a major contributor to her eventual descent into prostitution, and thus sickness and death.
Hugo wanted to portray the travesties brought down upon the poor and uneducated by an unforgiving society, but by contrasting Fantine with the Thenardiers, he is able to show that poverty does not necessarily lead to moral corruption (Fantine's prostitution notwithstanding).