"They explain this in the novel. Fantine can't afford to keep Cosette in town and she sees how well the Thenardiers care for their own daughters--it seems like a good fit to her."
They didn't do so well with Gavroche. In the book, wasn't he the son of the Thenardiers? I don't think they ever make that connection in the musical.
If anyone ever tells you that you put too much Parmesan cheese on your pasta, stop talking to them. You don't need that kind of negativity in your life.