Lets say a PC gets to choose a language, can they choose to learn to speak beast?
For instance they choose to play a Ranger with the UA Class Feature Variant Deft Explorer, the benefit Canny says:
thanks to your extensive wandering, you are able to speak, read, and write two languages of your choice.
Sadly not. The set of languages typically available to PCs is listed in Ch. 4 of the Players Handbook. Players typically select from either the Standard or Esoteric languages.
Standard Languages include Common, Dwarvish, Elvish, Giant, Gnomish, Goblin, Halfling, Orc as well as any regional language like Chultan.
Esoteric Languages include Abyssal, Celestial, Draconic, Deep Speech, Infernal, Primordial, Sylvan and Undercommon. These languages are typically learned by scholars, and are used by creatures from other planes for the most part.
Two languages known by specific classes would be Thieves Cant for rogues, which is more of a patois than a language, and Druidic for druids, of course.
Beast Speech is a feature of Forest Gnomes, which allows them to communicate with small animals, which notably do not have a language in their stat blocks.
If you look at the stat block for most beasts, such as a wolf, you'll see:
Languages --
This means that the beast speaks no languages. There is no language that you can learn that will allow you to converse with a wolf. For that you need magic (such as the speak with animals spell), or some other special ability.
However, there are a few animals that understand or speak one or more languages. For instance, a Giant Elk has the following:
Languages Giant Elk, understands Common, Elvish, and Sylvan but can't speak them
Also note that a giant elk's intelligence score is 7, which is well within the range normally considered sentient. If you wanted to be able to communicate with a giant elk, you could theoretically learn to speak and understand the giant elk language, which would allow you to speak to any giant elk and allow them to speak to you. You'll need your DM to sign off on such a plan, though, because giant elk is not on the list of standard languages. However, unless you are playing in a campaign that is heavily elk-focused, this is probably not a good use of your limited language selections, especially because the elk can already understand you when you speak Common.
According to the rules as written, you would normally be able to choose from Standard Languages, and with your DM's permission from the Exotic Languages list. These are on p. 123 of the Player's Handbook.
However, if you take up 2 levels as a Druid and choose Circle of the Shepherd (XGE p. 23), you will get the Speech of the Woods feature:
At 2nd level, you gain the ability to converse with beasts and many fey. You learn to speak, read, and write Sylvan.
In addition, beasts can understand your speech, and you gain the ability to decipher their noises and motions. Most beasts lack the intelligence to convey or understand sophisticated concepts, but a friendly beast could relay what it has seen or heard in the recent past. This ability doesn’t grant you friendship with beasts, though you can combine this ability with gifts to curry favor with them as you would with any nonplayer character.
For a full list of languages and further information this might be helpful, too:
