You are probably right about these particular jewels being considered state property at the time. Although it's also true, that in some cases the reigning families of each dynasty had to leave "in a rush" when the monarchy collapsed, so perhaps they had no time to think about how to take away various regalia. Since you are interested in Orleans, I don't know if you already read at the time of the news about this Louvre theft last year but one of the crowns that was stolen was made for Queen Marie-Amalie, wife of King Louis-Philippe, and sadly one of the items which may never be recovered. In fact some of the news I read suggests that many or all of these regalia will simply be taken apart for the value of the jewels/precious metals. Eugenie's crown was the lucky exception!

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Probably because they were the state's crown jewels and not their one private jewels.
After the abolition of the monarchy in Portugal, Queen D. Amélia took some years to recover all her private jewels.
Naturally, the portuguese crown jewels remained in Portugal.