The New Testament was written primarily in Koine Greek (the predominant language of the time, known by most people), but there are portions that were written in Aramaic (the primary language of the Jews in Jesus’s time), and Latin (the official language of the Roman empire).
Because it would have been the primary language of Jesus and his disciples, some scholars believe that some (if not all) of the New Testament books were written completely in Aramaic. The Aramaic version of the New Testament is called the Peshitta. However, most of the time when the New Testament speakers and writers quoted the Old Testament, they quoted the the Greek version of the Old Testament, called the Septuagint (LXX), so they undoubtedly could have considered writing in Greek for uniformity sake (though you could argue that the New Testament authors were writing for people and not with the intention of making an overall book).
Personally, I think that it’s quite possible that some of the New Testament books and letters were originally written in Aramaic (such as Matthew) and were soon translated into Koine Greek so that the Victorious News could reach a wider audience, or even vice versa. At the very least, there is still harmony between the Greek and Aramaic versions and both offer insights into the first century times and culture.