If you are going to age Champagne, you need very cool storage condtions. If you try to age it anywhere near normal modern household temperatures, I doubt if any Champagne will change for the better. The safest way to drink old Champagne is to buy an older LD one that is kept in the cellars of the Champagne maker as stored to age, and then separated from the lees, etc. shortly before shipment. The long contact wth the lees can give a special character that many like, and the Champagne may become more rounded. The main disadvantage is that most of the better RD Champagnes are quite expensive.
With very cool storage conditions, some have reported that some less expensive NV Champagnes will soften and round a bit with a year or so time in the cellar, but others may not.
There was, and may still be, a following for long aged Champagne in the UK. You probably need to start with a high quality vintage Champagne which must be stored under ideal, very cool conditions. I have tasted
1969 Krug that was long aged. There is no doubt that the Champagne changes. Some like the character of the aged Champagne, and others hate it. If things do not go right you can expect a dark, oxidized wine that is not fit to drink. If things go as they should, the wine will become a golden color, it will become more smooth, and it may have a nut-like quality. There may be much less sparkle for a long-aged Champagne.
If you are going to long-age Champagne, you first need to taste some. RD will not do, as it has a different character from what you get by aging normal Champagne that has been prepared for sale. I have no idea where you can buy old Champagne, other than RD, that has been aged properly. It would be a pity to long-age Champagne only to find that you do not like the style. Although the RD is expensive, it is far safer than aging Champagne yourself.
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