While Uncle Sam represents the American government, Marianne is the symbol of france as our homeland or mother land. It is the symbol of France itself and its motto since the revolution: Liberté, égalité, fraternité which means Freedom, equality, fraternity. The name Marianne was used for a number of reasons:

Marie and Anne were the two most common names for girls in the French countryside of the 18th century. The common peasants were at the origin of the revolutionary movement and the largest cast in France.
A song was published just days after the Bastille was taken. It was very popular and was called The Healing of Marianne
In the play “l’Avare” written by Molière (the French version of Shakespeare) more than a century before the revolution, one of the main characters was called Marianne. She represented freedom of choice against tradition and oppression
So Marianne became the symbol of freedom and of the new France the people had fought for. Until the Euro became our currency, we used “Francs”. Marianne was on every coin. She still is on very stamp we use. Take that Elizabeth Windsor :0) Just kidding, you know how much I love the queen