If we hop in to our Etymological Time Machine and steer it to ancient Rome, we'll see the word "genius" referring to a kind of local or familial spirit. Towns and gates had their own genius; so did clans, families, and individuals.
The concept lives on in the idea of personification (for example, "The Spirit of St Louis", the "Spirit of Christmas", Uncle Sam, the Statue of Liberty, and so on.)
The Genius of America, Adolphe Yvon, 1858
As for the word itself, it didn't begin to take on its contemporary meaning of "super-smart individual" until almost the 1700's, and even now I don't know if it carries this meaning in languages other than English. Its older meaning carries the idea of an essential spirit or character. It comes from the same root as "generate" and "genial", and is a cousin to the word "nature."
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The idea of "the feminine genius" takes my mind in so many different directions, I hardly know where to start. Certainly it involves giving proper respect to the vocations of mothering and childrearing. But how does the feminine spirit manifest in the lives of women who are married but struggle with infertility -- and may not be called to adopt children? For women who are single, who aren't mothers, who don't see Mr Right on the horizon but who don't feel called to religious life? How does that spirit play out for them? What about when the children grow up?
How does the feminine genius manifest itself in the workplace -- especially in a workplace that isn't part of the traditional teacher-nurse-housekeeper realm of women? (And how did some work come to be considered "women's work" anyway?) And are there ways that we should be taught to develop and express that spirit?