Who is she?

She is Mary Magdalene, the painting is called “Magdalene with the Smoking Flame”. It is said that they put this painting because Magdalene represents the lost bride of Jesus and is also the archetype of the "Sacred Feminine”.
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I read about this in the Da Vinci Code, it was very interesting.

Saint Mary Magdalen with the Smoking Flame is an oil-on-canvas by French Baroque painter Georges de La Tour, painted in 1640. This version of the painting is currently held and exhibited at the Louvre in Paris.

That looks like the painting from the little mermaid!