Being a single mother is hard in early 19th Century France. When young Cosette was traveling with her mother trying to find a job and a place to live, they were always shunned away because very few employers hire single mothers. When she is promised with the prosperity of working in the big city, Cosette is separated from her mother in the hopes a caretaker will watch over her while her mother earns some money. Unfortunately this was a trick and the caretaker is a corrupt man who makes Cosette his indentured servant. Then the kind mayor of the town that Cosette makes her new home in sees how winds of change are so detrimental for children and families, and decides to do something about it.
As you can guess from the title this series is a retelling of the classic Les Miserables tale meant for children. Although even though it's for children most of the things in the book haven't been toned down for the anime. With the exception of Cosette's mother having to work in a brothel, I didn't see anything that was remarkably different from the book.
In this anime, they have also done a very good job in getting you attached to the characters, especially Cosette and Gavroche. Also unlike the movie adaptions, they aren't restricted to just a couple hours to tell the whole story. They have time to develop the characters and time to tell the story more accurately.