Most champagne bottles I've seen have a rim and are capable. However they usually require larger 29mm caps, and a larger capping bell of course. I have a Super Colona (sp?) capper/corker and it came iwth a standard 26mm bell, 29mm bell, and corking attachment.
I've used the caps on champagne bottles and they hold carbonation fine. Reuse those big bottles
I have some champagne bottles that take 26mm caps so I use caps on those. For the larger-mouthed bottles I use plastic champagne corks and wire cages. I drive them in by hand. Most of the champagne bottles that originally housed beer are easy to get corked but actual champagne bottles often have smaller opening and it takes some serious pressure to get the cork in.