If you repitch anything (which you shouldn't need to) I would only repitch the same strain as the original. What happens if the champagne yeast can ferment the beer lower than the original strain after you bottle it.
I wouldn't pitch new yeast, and if you pitch something like champagne yeast, I would do it a few days-a week before bottling!
If I had 8 hours to chop down a tree, I would spend 6 sharpening my axe. ~Abe Lincoln