I'm no scholar but from what I've read, it would seem that the Picts had their own language, unrelated to Gaelic. Maybe there were traces of Gaelic mixed in with whatever language they did speak, which would have been picked up through early contact with the Irish especially in the west of Scotland. In the northeast, Pictish placenames are more like P-Celtic. Then we have Admonan's account of the life of Saint Columba, where he says that when Columba visited the Brude's court on the River Ness he needed a translator. From that, we might assume that the language spoken by the Brude wasn't the same language that Columba knew, which would have been Gaelic. Either that, or it was a dialect or accent that he couldn't understand. The same goes on today if you think of how much the English language and the Gaelic too that is spoken in Scotland varies so much in different regions. Sometimes they still have trouble understanding each other even if they are speaking the same language!

I like to think that the Picts spoke in their own tongue which was some ancient indigenous language that was even older than Gaelic, possibly even a leftover from the Bronze Age. Since we'll probably never know for sure, that's what I'll stick to for now!