Well, if you want to change text in images (sprites), then you'd have to create them for each language and put them as animation frames, which are changed upon checking what language the game is running in.
However, if you want to change actual text strings,
then i guess you could set text to a variable + string combination,
Scoredisplay set text to [Player.Score & Randomtextitem.Scorestring]
as opposed to
Scoredisplay set text to [Player.Score & " <- Your score"]
and change the string contents based on what language is used.
I'd probably do something lazy and store all of my text strings for a layer in a single object's private variables (probably not a good thing to do).
As for the actual way of storing what language is used, i'd say that a single global variable and usage of webstorage should be entirely sufficient.