One aspect of the museum (closed right now for renovation) is anthropological/ethnological. The above photo shows how out front, positive (ahem) non-Western stereotypes are reinforced (ahem) in the iconography of the building. This shows how condescending and now seemingly archaic the views of patriarchal European monarchies (even progressive ones like the Austrians) viewed non-Europeans. Thank God the anthropological/ethnological section is closed -- I've got huge problems with the presentation of non-Western people as "science", and it still happens way too often, Quai Branly's own rhetoric being an example. It's as archaic and hateful as phrenology. Even archeology presented as natural history is problematic. Eh.
The Mineral Rooms: 4 this size. I looked and looked for Bohemian garnets and Bohemian moldovite, thinking they would be there due to the historical Empire, but I couldn't find them. The meteor room was quite impressive, although this presentation I find is only responded to well by people who know what they're looking at, which I don't.
After quite a search (it turns out I was looking in the wrong x million-years-ago room), I found trilobites! They had quite a collection of these also, many preserved in 3D, I don't know how.