I'm reading A History of Chinese Civilization by Jacques Gernet. He writes that the language of Chu "belonged to a different linguistic group"and that its civilization was "a synthesis between autochthonous traditions of the 'barbarian' peoples of the middle Yangzi and the 'Chinese' traditions of the principalities of the center, the zhongguo." In what ways did it differ?
He also mentions that Yue and Wu were "no less distant." What about those? If I'm not mistaken Yue can also refer to non-Han peoples of southern China. Were their aristocracies not Chinese?
Unfortunately, we don't actually know what the spoken language would have been, exactly. What follows is an overview of each of the three, with the dominant positions given.
I got a little mixed up with this, and tried to clear up some of the confusion. But it's a topic that's rife with confusion on its own, so my apologies if I've botched anything in this answer.
the Chu 楚 language
What we do have are texts like the Chu Ci 楚辭, a book of Chu poetry, but since people were writing in the same style as Zhou, we are still given only hints in such texts. It's been pointed out, for example, that Laozi was likely a Chu speaker. Regardless, Chu did use Chinese characters, or rather their own variations on a non-standard system. You can see examples of Chu writing on old gold plates they are known for.
Chu is believed by some to have been a Sinitic language, related to Old Chinese. Others have felt strongly that it's not. Mei Tsu-Lin and Jerry Norman, both well regarded scholars in their own right, wrote on Austroasiatic (Mon–Khmer) features in Chu writings. It's possible that it was Sinitic, and it's possible it was Austroasiatic, and in either case borrowed heavily from languages belonging to the other family. Borrowing was incredibly common, and muddies the waters when we're trying to trace origins.
Chu's grammar in terms of word order was not the same as Sinitic languages, and is more in line with Austroasiatic. Lexical items were quite different as well.
So, Chu may have been Sinitic, but was likely Austroasiatic.
the Wu 吳 language
The same is said for Wu is as well, with people arguing both sides. Wagner believes it to have been Austroasiatic, or at least certainly not Sinitic.
Meanwhile Wu and Chu are and were believed to be related to each other, even if not Chinese languages. Wu had been annexed by Yue prior to this. The mixture of the languages of Chu and Yue and Wu are believed to have become a big part of a language called Jiangdong (江東), which later became a substrate language in the modern Wu language we have today. Meanwhile modern Xiang, the language spoken around Changsha, is argued to be largely based on Chu, though Xiang itself is also unquestionably Sinitic.
Like Chu, probably Austroasiatic.
the Yue 越 language
Yue, however, is not generally believed to be Chinese, and I don't know of a single person trying to make the case that it is. To make things all the more confusing, remember that Yue (越) here does not refer to the modern language group called Yue (粵 e.g. Cantonese) nor Wu to the modern language group called Wu (e.g. Shanghainese). So then, which language group did it belong to? Depends on who you ask.
Norman and Mei Tsu-lin believed it was Mon–Khmer
Sagart generally argues that Yue was Austronesian, but…
… has also suggested a possible Hmong-Mien connection
Others believe it was Tai-Kadai / Kam-Tai
The problem with all of this is that we're going by reconstructions of Chinese and reconstructions of Austronesian, both of which we feel pretty good about, but then the material we have in Chu or Wu languages is pretty minimal, and not written out in a detailed system of phonological transcription.
It's quite hard to look at place names and names of people, especially since both changed often enough (even for a single person, even if they weren't alive anymore). So trying to work backward from the name of a village and then say 3000 years ago what language they spoke is pretty frigging complicated. It gets more complicated when we start looking at linguistic substrata as justification. Regardless, the jury is still out on exactly what sort of language family we're looking at for Chu and Wu, but not so much for Yue, at least in terms of thinking it might be Chinese.
I personally like Austronesian idea for Yue, but have no dog in that particular fight.
What about those? If I'm not mistaken Yue can also refer to non-Han peoples of southern China. Were their aristocracies not Chinese?
They were certainly not Chinese, and their kings were also not Chinese. Neighbouring states often are only discussed in sources other than their own, in terms of what we have access to today. So exonyms are quite common. We don't necessarily know what these groups would have called themselves, but can assume that just because they have a Chinese* name it doesn't mean they were Chinese themselves.
There are also some who argue that Zhou was not speaking a Sinitic language either, for what that's worth.
See also:
Dong 2014 A History of the Chinese Language
Knechtges 2010 Ancient and Early Medieval Chinese Literature
Norman & Mei 1976 The Austroasiatics in Ancient South China
Sagart 2008 The Expansion of Setaria Farmers in East Asia: A Linguistic and Archaeological Model
Sun Chaofen 2006 Chinese: A Linguistic Introduction
Wagner 1990 The language of the ancient Chinese state of Wu
