The figure of Marianne is the popular emblem of the French Republic, as such she represents the state and its values of liberty, equality and fraternity.
Although her image is found on stamps, French euro coins and all government stationary, neither Marianne nor the gallic rooster enjoy official emblem status. The French constitution only recognises the French flag as the official state emblem.
The 1830 oil canvas by Eugène Delacroix entitled "La Liberté guidant le peuple" depicts Liberty, personified by Marianne, leading the people to victory during the French Revolution of 1789. The Phrygian cap she wears in the painting had come to symbolise liberty during the revolution.
Yes, Coldplay also used this painting as part of the artwork for their fourth album.