naïve is the correct and official spelling/writing but naive is accepted, mostly because people can't be bothered putting the two dots on the i.
orthography - Is it spelt "naïve" or "naive"? - English Language ...
If "naive" has become an English word, is the accent still compulsory? (I'm sure there are examples of foreign words whose accents have atrophied away as they become English words) This is where you need to reach for the reference books. For example, the "Oxford Writers' Dictionary" gives naïve as the correct form.
Naive has a more neutral connotation and generally indicates a person who isn't familiar with the way the world works. Naive can sometimes even have a positive connotation and mean someone who hasn't been jaded by the negative realities of the world. Naive people are likely to be trusting or unsophisticated.
If the person is unable to function in a given setting because of a lack of knowledge- that person is ignorant. If the person believes everything they're told without a healthy amount of skepticism and "common sense" that person is naive.
Hitting it straight off here, naïve is a loan-word (a word that was derived from another language yet has avoided entire english assimilation) yet naivety is an english modification to the word. Changing the word to english rules force the word into a completely english state, removing the dieresis (¨) from over the i. In addition, personal experience leaves me hearing the word naivety as ...
The origin of "naive" is the French word " naïve ". (Notice that the French " naïve " is italicized) As a French word, it is spelled naïve or naïf. (French adjectives have grammatical gender; naïf is used with masculine nouns while naive is used with feminine nouns.) The two dots above the "i" are called diaeresis. As an unitalicized English word, "naive" is now the more usual spelling ...