After watching "The Collector", I'm not a fan of this one, but there are three specific points to debate here- Nathalie, Mrs Agreste, and Audrey Bourgeois (whose theory page is here). Don't derail by talking about why she could be Mrs Agreste here, this is points for why or why not Le Paon is Nathalie. Keep it about Nathalie.
Remember to tag your spoilers, please.
So, Nathalie. We know she works for Hawk Moth, and she knowingly works for him. She knows Gabriel is Hawk Moth. She knows about the Miraculouses. It is thus possible to say that she desires the power herself and steals the Miraculous from the safe (or something, assuming the one in there isn't a fake) and becomes Le Paon. If it is a fake, she could have swapped them ages ago.
Now, my theory is that Nathalie and Mr Agreste actually know full well where Mrs Agreste is. Her "disapperance" is a lie they tell to Adrien to keep him out of the Miraculous business. Mrs Agreste is somewhere else, researching into the Miraculouses, and Gabriel took back the Moth and Peacock Miraculouses and the Book to protect them. Nathalie is in on it, too, and she knows a bit about the Miraculouses because of it.. At some point she stole the Peacock Miraculous and replaced it with a fake- a possible chance would have been in "Simon Says" when she's alone in the mansion, I suppose, after Gabriel was taken away and the Gorilla was one of Simon Says's minions. I think "Simon Says" happens late in Season 1 chronologically, but there's also a chance she has not yet stolen the Miraculous nor had the idea to steal it yet.
Personality-wise, Nathalie could be hard to akumatise because she's emotionless, though it's very possible she is the red and black akuma. For the sake of the theory, she lets herself be akumatised for the same reason as Gabriel did. Nathalie is so emotionless she might actually do well for being Le Paon.
As to a motive, she could be tired of taking Gabriel's orders, she could just want the power for herself, or she could have an actual goal, possibly related to Mrs Agreste or the other Miraculouses. We know so little about her, it could be anything.
I'm not sure how much I like this theory- I think the fact that she's in on the Hawk Moth thing automatically disqualifies her because she'd be his primary suspect since she has access to it and I don't think akumatising her would change that unless she can somehow make Le Paon appear to him anyway. The fact that she'd be his primary suspect for the theft is followed by the fact that she appears to get akumatised. I don't think Le Paon will be akumatised. They can't show that Hawk Moth can have control over her for their power dynamic to work. I also think being emotionless would backfire on Nathalie, because showing emotion at all would get the akuma to go after her. I also think that her getting akumatised on purpose carries a totally different weight to it than Gabriel doing it. Her doing it proves nothing other than Hawk Moth can control her.