Naïf - naïve - naïveté
Naïf, naïve and naïveté (together with their derivatives) are all forms of a French adjective, naïve, which has been taken into English (so much so that it is used without the diaresis, naive) with the basic meaning "natural, unaffected, simple, artless" (OED). A person who trusts someone whom s/he should not trust (e.g. the duck in the children's story Jemima Puddleduck, by Beatrix Potter, who trusts a fox,) can be naive. naïve painters like the American Grandma Moses, or the French Douanier Rousseau, are those who paint pictures without any academic training in their art. Sometimes their paintings or drawings are very like those of a very skilful child. (For a note on the pronunciation of these words, see Naïf - pronunciation.
The adjective naïf (or naif) is the masculine from of the French adjective. In French, a too trusting man is naïf, a too trusting woman naïve. This is not a distinction I would recommend in English, where adjectives have no inflections. But it is to be found in some academic writing. (Oddly, I cannot remember seeing the adjective with either of its plural inflections in English - neither
'naifs' nor 'naives'. This seems quite a good reason not to use the gender specific inflection either.)