Catherine-Thérèse de Matignon Thorigny (1662 - 1699) married Jean-Baptiste-Antoine Colbert (1651 - 1690), Marquis de Seignelay in 1679. He was the eldest son of the great Colbert and immensely wealthy. The marriage produced five sons.
The marquise was widowed the year before this picture was painted. The children shown in this portrait are probably the eldest, Marie-Jean Baptiste (1683 - 1712) and possibly the youngest Théodore-Alexandre (1690? - 1695?). The marquise is shown as the marine deity Thetis, and the elder child as Achilles, the son of Thetis. The child at the right is shown as Cupid, but it is not certain that he was meant to represent Théodore-Alexandre or any of the marquise's other children.
From The National Gallery Podcast: Episode Forty Eight, October 2010