They say that Basque, Finnish, and Hungarian are of uncertain origin. Not Indo-European anyway. That might put them in a non-Celtic category.
They probably came from the same stock as all the other Indo-Europeans, just earlier and arrived through the Middle east. I suspect they became isolated in Spain - France during the LGM, 18-23,000 years ago and were joined by the rest of the 'family' after the LGM by a group arriving through Russia.