What languages did Josephus speak? He lived in the land of Israel during the first century CE. He wrote in Greek (so he obviously knew that), but did he know Hebrew, Aramaic, or Latin?
Josephus knew Aramaic, Hebrew, Greek, and Latin (which he must have learned when he was in the service of the the Roman Emperor Vespasian, if not earlier). A quick look on JSTOR turns up this article for reference.
In Tessa Rajak's book "Josephus" (Appendix 1), she considers whether Aramaic or Hebrew was his primary language. She concludes that, while we cannot know with certainty, the evidence implies that he was equally capable in both languages.
Josephus was able to read and write in several languages.
Also, parables in the Talmud and Mishnah are always in Hebrew. Even when the Talmudic text around them is Aramaic, the parable will be in Hebrew. Parables were sermon illustrations meant to be delivered to the common person.
Specifically from Josephus on his language, we read:
Josephus in Antiquities 10 1.2 says this: "When Rabshakeh had made this speech in the Hebrew tongue, for he was skillful in that language, Eliakim was afraid lest the multitude that heard him should be disturbed; so he desired him to speak in the Syrian tongue." This is an event from the Old Testament, but Josephus uses the same words to describe the language spoken by Rabshakeh as he does to describe his own language and that of his fellow Jews. He does not say that now they speak the Syrian tongue.
Josephus (War 5 6.3) points out that Jewish soldiers used a play on words that only makes sense in Hebrew. In 6.3, whenever a stone was on its way (being thrown from ballistea), the watchmen would shout "in their native language, 'The Son Cometh!'" While translators are confused by the Greek text, the answer makes sense in Hebrew. Whiston, the translator, admits how the words could be confused in Hebrew but not Aramaic. The watchmen would have shouted, in Hebrew, Ha-even ba’ah ("the stone is coming!"). However, because of urgency, the words would be clipped to ben ba ("son comes!").* They reduced the syllables due to time constraints. This pun is known in Hebrew and even appears in the NT (Matthew 3:9 and Luke 3:8) "God is able from these avanim [stones] to raise up banim [sons] to Abraham."
This wordplay is unambiguously Hebrew. In Aramaic, the phrase would be kefa ate ("the stone is coming") or the more literary avna ata. Neither sounds like bara ate ("the son is coming"). Another option for Aramaic would be to use the word aven, which is related to the Hebrew. However, aven would change the gender of the verb and still not work to make a pun on "son," bar.
*Similar to how modern soldiers reduce "Enemy fire incoming" to simply "Incoming!"
In Wars 5 9.2, Josephus tells how after he was captured, he was sent as an envoy to negotiate his people's surrender. "And being sensible that exhortations are frequently more effectual than arms, [Titus] persuaded them to surrender the city, now in a manner already taken, and thereby to save themselves, and sent Josephus to speak to them in their own language; for he imagined they might yield to the persuasion of a countryman of their own."
As Josephus just established through the use of the pun that the soldiers were speaking Hebrew, it stands to logical reason, that he too spoke Hebrew.
It should also be noted that Josephus refers to biblical words many times and explains what they mean in the Hebrew/Jewish tongue/language (i.e. Contra 2.2, Anti 1 1.1,2 (2x); Anti 5 2.2). At times, he explains these biblical words by saying "in our own tongue/language" (i.e. Wars 6 10.1, Antiquities 7 1.3). (There are many other examples of the above.) Logically, Josephus is drawing a connection between the language spoken by Jews in the Tanakh period and the common language spoken among his people of that time.
Language spoken by Josephus: Aramaic
Jewish Historian Josephus wrote –
Jewish Wars (Book 1, Preface, Paragraph 1):
In Antiquities of Jews Book 3, Josephus points out that Hebrews called Pentecost "Asartha." Asartha is Aramaic, because Aramaic places the definite article ("the") at the end of the word, thus the 'tha' at the end of 'Asartha' is the Aramaic definite article on a feminine noun. This is the same thing with the Aramaic words in Bible like Gabbatha (John 19:13) and Talitha (Mark 5:41). The 'tha' at the end of 'Talitha' is the Aramaic definite article on a feminine noun.
In first century AD, Jews called Aramaic "Hebrew", because that is the language of Hebrews. Jews are also called Hebrews, because they are the descendants of Abraham the Hebrew (Genesis 14:13, Philippians 3). If it was Hebrew, then definite article of Hebrew would have been in the beginning of the word. If Josephus was writing Hebrew, then the word "Asartha" would have been "Ha Atzeret." Like Hebrew, the definite article ("the") of English is at the beginning of the word. We say "the car." We never say "car the."
That is why NIV, ESV, and other bible versions write the words like "Gabbatha" "Golgotha", etc. as Aramaic instead of Hebrew.
John 19:13 (NIV):
Even today, Many Iraqi Jews call their Aramaic "Hebrew" ("Ibraith" in Aramaic), because it is the language of Hebrews. So when Jews said "Hebrew" in first century AD, they are referring to their Hebrew tongue which was Aramaic in first century AD. We call Deutsch "German", because it is the language of German People.
Another point that should be noted is Old Hebrew was preserved through scrolls in first century AD, because it is considered as the holy language among Jews. High Priests preserved Hebrew scrolls for religious purposes in temple of Jerusalem.
But the spoken language of Israel was Aramaic (Gabbatha, Golgotha, Asartha, etc.) in first century AD.
According to the Talmud, there were silver trumpets in the temple into which people deposited their offerings. It must be noted that the offering trumpets were labeled in Aramaic, which is not surprising since they are dealing with money! When it comes to getting their money the Temple establishment made sure that these ornate offering buckets were inscribed in the language they spoke - Aramaic. Peshitta Tanakh is first century Old Testament written in Aramaic.
Just like Jews preserved Old Hebrew for religious purposes in first century AD, many Hindus preserve Sanskrit in Kerala (a state of India) for religious purposes, because it is the holy language of Hindus. But the spoken language in Kerala is Malayalam.
Another thing that must be noted is Judean Aramaic was also known as Hebrew in order to differentiate the way Aramaic is spoken in Judea and Aramaic spoken in Galilee and Syrian regions. Aramaic in Syrian regions was called Syrian tongue while Aramaic in Judea was called Hebrew tongue.
Through Matthew 26:73 and Mark 14:70, Peter was exposed by his Galilean Aramaic speech among people. Judeans used Dead Scrolls Alphabet to write their Aramaic while Syrians commonly used Estrangela Alphabet to write their Aramaic in first century AD. The Galilean accent of Aramaic would have sounded to the Judean Aramaic somewhat like Cockney sounds to a British aristocrat. In Talmud, Galileans are ridiculed for the way they spoke Aramaic in Galilean regions.
Also note the names in English Bible of New Testament - "Bar"tholomew, "Bar"abbas, "Bar"nabbas, "Bar"sabbas, "Bar" Jesus, Simon "Bar" Jonah, "Bar" Timaeus, etc.
Aramaic word Bar means Son. In Hebrew, Ben means Son. Even Rabbis point out that "Bar" in Bar Mitzvah comes from Aramaic.
In Josephus' Jewish Wars, one of the top 3 leaders who fought against Romans was Simon Bar Giora. Bar Giora means "Son of a proselyte" in Aramaic.
Also notice the name "Cephas" in New Testament Bible.
John 1:42 (ESV):
Galatians 2:9 (NIV):
Cephas is also mentioned in 1 Corinthians 1:12, 1 Corinthians 9:5, 1 Corinthians 15:5, etc.
Cephas comes from Aramaic word Kaypha which means stone.
Till 130 AD, Aramaic was the spoken language of Jews. From 131 AD through the rise of Bar Kokhba and Bar Kokhba revolt (132-135 AD), the beginning process of reverting back to Hebrew occured. Although Aramaic was spoken by Jews from 131 AD to 135 AD, still they were encouraged to bring back Hebrew as their spoken language instead of Aramaic. This is because Hebrew is considered as the holy language of Jews.
After Bar Kokhba revolt in 135 AD, Jews continued to revert back to Hebrew. By the end of second century AD, Hebrew was a common spoken language among Jews.
Famous Israeli Archaeologist Yigael Yadin who received Ph.D for his researches on Dead Sea Scrolls noticed this shift from Aramaic to Hebrew through his researches. In "Bar Kokhba: The rediscovery of the legendary hero of the last Jewish Revolt Against Imperial Rome" Yigael Yadin notes, "It is interesting that the earlier documents are in Aramaic while the later ones are in Hebrew. Possibly the change was made by a special decree of Bar-Kokhba who wanted to restore Hebrew as the official language of the state" (page 181).
According to Wikipedia (although there is no reliable ciation), Josephus spoke Aramaic, Hebrew, and Greek.
Not a complete answer, but according to Wikipedia, which quotes his Bellum Judaicum, his paternal tongue was probably Aramaic.