What's the best way to say "Chinese speaker" in Chinese? There are the terms 母语者 and 非母语者; there are 华语学者 and 中国通 and 能说中文的人. None of these terms seems to encapsulate the simple "Chinese speaker," meaning "a person who speaks Chinese," in Chinese...
I think the challenge lies with how the English word "speaker" does not translate well to Chinese, in the context you describe.
From the dictionary, we can see that speaker in the sense of language ability simply translates to 說。I would argue that adding 會 or 能，thereby making it 他會說法語 or 他能說法語 , is giving more information than required. Perhaps depending on context, it would be necessary to respond this way, but a simple 他說法語 is a short and complete sentence on its own.
Also, I would like to point out that there are certain pockets of the world where "Chinese" refers to both Mandarin and Cantonese, and a follow up question to "Do you speak Chinese?", is, "Which one?"
In certain industries, multilingual employees will wear badges indicating what languages aside from standard assumed (Eg. English in North America, Japanese in Japan, etc.) can be used for conversation. Sometimes, instead of just the name of the language, you can see "精通" as well. While it should translate to proficient, that's often a generous description and should actually be taken to mean "conversational in". Truthfully, "通曉" would be a better description.
On that thought, "通" could be what you're looking for if you're looking to describe someone's ability on paper. Think of an online dating site. A possible description could be: 女，25-35歲，通國、粵、英語。
Going back to the problem of "speaker" not translating well to Chinese for a moment, notice that there isn't a single character to mean "person orating" or "person giving a speech". See the dictionary link above. In Chinese, you typically need three characters; 演說家、演講者、說話者, with the last one being awkward but proper in my opinion.
We do not express like that.
We never say “He is a Chinese speaker” in Chinese. There is not a grammatically correct Chinese expression for this English expression. We can only say:
He speaks Chinese.
Also, you can use a weird but grammatically correct expression in Chinese:
He is a person who speaks Chinese.
The term “speaker” does not exist in Chinese. If you search in an English-Chinese dictionary, "speaker" is translated to 说……的人 (literally, person who speaks ...).
The expressing culture and grammar are different in different languages. Some English-style expressions do not exist in Chinese, so you may need to change the sentence patten in order to make it sound normal in Chinese.
By the way, some Chinese-style expressions do not exist in English either, for example, it cannot be asked about the ordinal number of a president in English
What ...th president of the USA is Donald Trump?
The 45th president.
while it can be asked normally in Chinese
In Chinese context, if someone was mentioned as 说中文, it generally means a person who can speak mandarin. The bottom like will be general literacy was relative new thing in China history. Speaking some form of Chinese dialects like Cantonese is totally different from that he can read/write Chinese character.