'Ba mhaith liom labhairt le Máire' = 'I would like to speak to Máire'.
I have heard somewhere, can't remember where, so don't know if it is reliable, that 'caint' is talk and 'labhairt' is speak. They seem to be interchangeable in English or perhaps misused? Anyway, bottom line is I am confident my use of 'labhairt' above is correct, but am unsure about when to use 'caint'.
(By the way, 'saoirse labhartha'
means 'freedom of speech'!)
Nothing wrong with
Ba mhaith liom caint le Máire
Gaeilge labhartha = spoken Irish
an teanga a labhairt = to speak the language
... but pretty much interchangeable in many cases I would say...