"Loving beauty is female's natural instinct"
"a natural instinct of female" sounds slightly better to me, but I would use "women" rather than "female".
I find "loving beauty" a bit questionable, as (in my opinion) the instinct is to be beautiful themselves, not looking at or possessing anything beautiful.
So I would phrase it like these.
1. Wanting to look beautiful is a natural instinct of women.
2. It is a natural instinct of women to want to look beautiful.