Naive and native are the same Latin word, borrowed twice.
The source is Latin nativus, "born, innate, natural," from natus, the past participle of nasci, "to be born." English took it once, in the late 14th century, through Old French natif. That became native, first meaning inborn or hereditary and, from the early 15th century, born in a particular place.
French kept wearing the word down. By the 13th century Old French naif had a wide spread of meanings: natural, genuine, just born, unspoiled, and also foolish or innocent. A newborn is natural and genuine, but it also knows nothing, and the word covered both sides.
English borrowed it again in the 17th century, this time as naive, meaning natural, simple, unsophisticated and artless. Merriam-Webster dates it to 1614, Etymonline to the 1650s. It arrived as a fashionable French import. In Dryden's comedy Marriage à-la-Mode (1673), naive and naiveté are among the French words that Philotis brings Melantha to enrich her conversation.
The form English chose is the French feminine, naïve. The masculine naïf came in too, recorded from the 1590s, but English uses it without regard to gender. Grammarians noticed. In 1893 William B. Hodgson complained about writers applying the feminine naïve to men and women alike, an error he called "almost universal though not quite."
The word kept its French look. Dictionary.com lists naïve, with the two dots, as an accepted variant. In French the diaeresis marks the i as a separate vowel, which is why the word has two syllables, and many English writers keep it.
Over time the meaning narrowed. Dictionary.com's first definition is now lacking experience, judgment or information, credulous. The older, kinder sense survives in art, where naive describes a direct style by painters with little formal training. Science has its own use: an animal not previously used in an experiment is naive.