Are you supposed to swirl Champagne?
No. But don't let me stop you. Just be careful in that evening dress if the flute is too full.
You want to avoid swirling mainly so as to preserve maximum carbonation – the tiny bubbles you paid so handsomely for. Will a quick swirl or two wreck your wine? No. I sometimes make a point of swirling sparkling wines that I find are too frothy to begin with, simply to smooth them out to a flatter and more sippable state.
With still wines, the point of swirling is to get the liquid to climb up the sides of the glass, thereby increasing the evaporation surface in order to amplify aroma. With sparkling wine, that's not as critical because effervescence does much of the air-lifting – so to speak – for you.