The set of text files is clearly countable because it's made of binary. Do you think you can make an English sentence that can't be written into a text file?
If humanity lives forever, it will keep on inventing new words and therefore new sentences. So the question of whether or not language is finite is really the same question as whether or not the universe is.
> If humanity lives forever, it will keep on inventing new words and therefore new sentences.
That just increases the fraction of text files that count as "English". Which doesn't affect the argument.
> the question of whether or not language is finite
does not need to be answered. If English has a thousand words and never gains another one, the list of English sentences is countably infinite. If English gains 10% more words every year forever, the list of English sentences is still countably infinite.
