It is my speculation that Nathalie is both the Peacock Miraculous holder AND Mrs. Agreste. Something tragic happened some years ago and she lost her heart/memories, hence her name: Sancoeur. Gabriel Agreste, Le Papillion, believes he can restore her with the power of the black cat and ladybug miraculouses. In the meantime she acts according to instinct to look after her husband and son, but cannot feel anything--or her feelings are strongly suppressed. When she has her miraculous she becomes insane or unstable, and so he took it from her and keeps it behind her portrait.
If you observe their features, you will find she has the same facial structure (especially nose/bridge, chin). The prime differences are hair color and eye color, with the minimal difference of having her hair pulled back into a bun and parted in the opposite direction. The former factors could be magically altered, or just hair dye and colored contact lenses. The change in hair and use of glasses among these other factors could be Gabriel's attempts to hide her true identity from the public. Given his high publicity, it would be dangerous for people to speculate. Her eyes do not fit perfectly, but that is because they are in a placid, drooping melancholy, whereas Mrs. Agreste's eyes were bright and full.
Also, the portrait of Mrs. Agreste has peacock eye-like designs all over her body, though they are subdued by the abstract art style. If you go through the gallery and compare their features you will certainly perceive resemblances. Gabriel notes that his wife was sensistive, while Nathalie is cold. Also, the name Nathalie means "born on Christmas." Given that the Agreste household does not celebrate Christmas and Adrian has a specific angst associated with that holiday, the incident may have coincided with Christmas. Notice in the portrait how Mrs. Agreste is covered in pearl-like beads. Nathalie wears earings of this same nature.
It's just an idea, but I think it fits really well. The heartless Mrs. Agreste is sitting right under our noses this whole time. Maybe Adrien's allergy to feathers is actually psychosomatic.