The language clearly has (a) gendered 3rd person pronouns and (b) gender-neutral ones. This eliminates all of the Romance languages -- no gender-neutral pronouns to be found there. It also eliminates most of the world's languages by count -- dividing nouns into classes is a common feature; calling classes "genders" is unique to the Indo-European language group (and AFAIK, possibly just the "European" subgroup).
While Greek has three genders, if I had to guess, I'd guess a Germanic language. Hey! English is a Germanic language!