- I can not find any official statement that Aquaman can speak any language on Earth.
- In addition to the languages you mention we also saw him speak Icelandic in Justice League.
- Regarding the film, I think the Atlantean language is a sort of parent language.
- There are a few Atlanteans that we see understanding other languages.
- I would argue that all Atlanteans, not just Arthur speak multiple languages...
The comment from @Shreedhar is likely such as there is no official source. It is a comment made by the author of the article found here. In addition, DC's official sources make no comment of his ability to speak multiple languages. It is mentioned in the link that Aquaman's telepathy is limited to communication with aquatic creatures, so that is not a basis for any universal understanding.
Regarding the film itself I would argue that the Atlantean language seems to be a sort of parent language that many (if not all) other languages are derived, making it easier for them to understand other languages. I can not find much proof regarding the Atlantean language as far as DC is concerned, but using only details from the film I think there is enough to validate my deductions! (I am also using the assumption that anytime Atlanteans are speaking to one another we are just hearing English for sake of the movie and they are speaking their native tongue...)
Obviously the primary case is Arthur himself as we see him speak quite a few languages throughout the film as you point out; there is another language he speaks we learn from Justice League when he first meets Bruce in the Icelandic village, though I am unsure what language it was...
From Arthur's mother and father I think we can safely assume he would have learned Atlantean, English, and Maori. Anything beyond these I would say he would have needed to "learn" on his own. However, growing up on land and his travels may have prompted him to go out of his way to "learn" the extra languages and they may not be effortlessly understood using Atlantean as a base.
With that counter point, the other main case I would argue would be Atlanna herself. When she first meets the lighthouse keeper we see she is able to understand him and communicate with him speaking English. However, she seems to know nothing else of his customs or lifestyle. She believed the fish tank was a feeding dish, the pet/dog was a strange sight to her, and the television was completely foreign to her as well.
It seems odd to me that she would have been taught one language of the "surface dwellers" (why just English?) and yet not understand anything beyond the language. In the process of learning other languages I would expect at least some excess details to be divulged either from the mind set of "Can you believe they do this?" or "This word has no meaning to us but it means this to them?"
Another case from the film regards Mera. When she and Arthur travel to Sicily she interacts with a small girl who brings her a book about Pinocchio, referencing the previous mention from earlier in the movie. I would assume this book was written in Italian given the location. From this interaction I believe it is safe to assume Mera can understand Italian.
Lastly, Orm was able to speak with Black Manta, using the water hologram technology though I suppose there could have been a concealed translator in the technology so this would be the weakest example on its own... Kind of related, Black Manta speaking with the elite commandos tasked to him could fall into the same case of a translator being used during communication...
I believe these are all the examples from the film of Atlanteans speaking to "surface dwellers" in their own native tongue. Obviously there were no chances for this while underwater and these examples only involve High Borns so it is possible that the High Borns are simply know or learn other languages. Without more details from comics or future films I think we can safely say for now that Atlantean is the key to the characters' understanding of other languages and it is safe to say all Atlanteans are or have the potential to be universal polyglots.