I am very attached to my headcanon that once he's king, Hiccup starts learning EVEN MORE languages (I picked Russian because it's the foreign language I've studied the most (I'm very bad though), and a few of the books mention the Rus . . .)
It's based on my own experience with recovering from a difficult period, especially when you feel like you've lost yourself: it helps to revisit something you know you like (and if he's fluent in Dragonese, French, and Latin, then Hiccup definitely likes learning languages), and it also helps to patiently work on learning something new. So I think Hiccup would try to pick up a few new languages after the war. And this time he can do it with library books! (who knows how he did it originally . . .)
edit: For those wondering what he's saying in Russian, he's practicing the singular and plural forms of Russian "cases," which are modifications you make to nouns in some languages to denote what part of the sentence they're acting as (i.e. direct object, indirect object, location, thing that owns something, etc.) The best way to practice cases is placing a word in a bunch of different sentences so that you're not just declining (modifying) them without context, but actually using the case in a way you might for a real conversation. In this case, he's practicing by putting the Russian word for "dragon" into the six Russian cases.
Transcription of my TERRIBLE Cyrillic handwriting + a translation under the cut for anyone curious:
