In a saucepan, combine the butter and shallots. Sauté for 2-3 minutes. Add the champagne. Bring to a boil and cook until almost all liquid evaporates, about 6 minutes.
Add the heavy cream, bring to a boil and simmer until cream thickens and coats the back of a spoon, and is reduced by nearly 50 percent in volume, about 3 minutes.
Whisk in the butter until smooth and strain the sauce through a fine mesh strainer. Season with salt and pepper. Serve immediately over salmon.