Freezing Champagne to keep its bubbles? Ummm, doesn’t really work.
WARNING: Unnecessarily lengthy post 
See, gases become more soluble at lower temperature, yes, meaning that the cooler a sparkling wine becomes, the slower it releases its carbon dioxide. That’s why keeping a bubbly in the coldest corner of the fridge makes sense.
However, if you have never frozen carbonated beverages, there’s this one little caveat that prevents bubbles from staying in a frozen medium. See, carbon dioxide (that has been put in there by high pressure) escapes from liquid through nucleation points, which are typically tiny imperfections in the glass. However, the moment a liquid starts to freeze, you get a HUGE amount of nucleation points from the sharp little ice shards and suddenly the carbon dioxide starts to escape more rapidly from the beverage.
Furthermore, when the pressure goes down, the temperature goes down as well, due to auto-refrigeration*. Usually this isn’t a problem with opened sparkling wine bottles, as the change in pressure is so small that the temperature change is negligible - but it still doesn’t do anything to stop the formation of ice, which rapidly depletes the from any CO2. There’s theoretically nothing to keep CO2 from getting frozen along with the wine, but the fizz in the wine is something that is kept there under pressure and the nucleation points from ice make sure that any extra CO2 that might give you bubbles escape the wine before it gets fully frozen.
*The bigger problem with auto-refrigeration is with unopened sparkling wines that have been chilled in a freezer. As sparkling wine bottle gets cooler, its internal pressure goes down as the solubility of gases increase (due to how less and less CO2 wants to escape from the wine as it gets colder). However, as soon as the first ice crystals form, the internal temperature skyrockets as now there are tons of new nucleation points that facilitate CO2 escape - which suddenly becomes greater than the drop resulted from the increased gas solubility.
When you open the sparkling wine bottle, the internal pressure drops from around 5 to 7 bar to around 1 bar. If a wine is at this delicate point where it is is just around freezing point, this kind of drop is more than enough to bring down the temperature of the wine from around freezing point to well below freezing point, which creates an interesting runaway chain effect: the carbonation escapes violently from the few ice crystals in the wine, which drops the surrounding wine temperature, making it freeze more rapidly, making the carbonation escape from the wine more rapidly, freezing the wine more, pushing the carbonation more, etc.
Suddenly your seemingly liquid sparkling wine gushes out from the bottle in an instant and all that remains is about half of the wine in the bottle as a solid ice chunk. Have seen this happen once to a sparkling wine and multiple times to a soda bottle. These things can be quite commonplace as people put stuff outside to chill in the wintertime when it normally is -5 to -20°C (25 to-5 °F) around here.
If the sparkling wine bottle is not strong enough, usually the very first formation of ice crystals can be more than enough to raise the internal pressure so high that the sparkling wine bottle explodes at that point. Normally you don’t have to wait for the wine to freeze and the expanding ice to break the bottle - it’d be much easier to just collect the broken pieces of glass and put the frozen wine chunk into the sink to that. No, normally the bottle explodes when 99,9% of the wine is still liquid, spraying the insides of a freezer with wine, making the cleaning process much more arduous! 