I would like to know exactly what language you speak.
The structure in the original seems to be wrong. It should have been:
Gostaria de saber corretamente (exatamente, ao certo) a lÃngua que você fala.
That's a wrong use of the sentence structure in Portuguese, not unusual though.
I see no problem (or inversion) in the original text. The requester is asking which language someone speaks fluently (i. e., without committing mistakes).