All we know is that if a language is countable than it must be recognizable. However, a recognizable language may or may not be decidable.
Your premise is incorrect. The set of all words, $\Sigma^*$, is countable (as long as the alphabet is countable, and we usually refer to finite alphabets anyway).
Every language is a subset of $\Sigma^*$, and thus every language is countable. In particular, there are undecidable and unrecognizable languages.