Add the sugar in an even layer over the bottom of a heavy saucepan, with a capacity of at least 2 or 3 quarts. Heat the sugar over medium-high heat, whisking it as it begins to melt. You'll see that the sugar will begin to form clumps, but that's okay. Just keep whisking and as it continues to cook, they will melt back down.
Stop whisking once all of the sugar has melted, and swirl the pan occasionally while the sugar cooks.
Continue cooking until the sugar has reached a deep amber color. It should look almost a reddish-brown, and have a slight toasted aroma. This is the point where caramel can go from perfect to burnt in a matter of seconds, so keep a close eye. If you are using an instant-read thermometer, cook the sugar until it reaches 350 degrees F.
As soon as the caramel reaches 350 degrees, add the butter all at once. Be careful, as the caramel will bubble up when the butter is added. Whisk the butter into the caramel until it is completely melted.
Remove the pan from the heat and slowly pour the cream into the caramel. Again, be careful because the mixture will once again bubble up ferociously.
Whisk until all of the cream has been incorporated and you have a smooth sauce. Add the fleur de sel and whisk to incorporate.
Set the sauce aside to cool for 10 to 15 minutes and then pour into your favorite glass jar and let cool to room temperature. You can refrigerate the sauce for up to 2 weeks. You'll want to warm the sauce up before using.