The wire wrapped around the cork of a champagne bottle is called a muselet.
The muselet is actually a metal cage, typically made of steel wire, that holds the cork in place against the pressure inside the champagne bottle. Champagne can be under a significant amount of pressure, around 6 atmospheres, which is three times the pressure of a typical car tire! The muselet is crucial for keeping the cork securely fastened and preventing the champagne from exploding out of the bottle.