In a 3- to 4-quart pan over medium heat, stir sugar and 1 cup water until sugar is dissolved. Increase heat to high and boil without stirring until mixture is a deep caramel color, 12 to 20 minutes. When sugar begins to brown around edges of pan, swirl gently to ensure that the mixture caramelizes evenly. Remove from heat and immediately add 1 cup cream (mixture may splatter); whisk until smooth. Pour into a large bowl and let cool to room temperature, about 20 minutes.
In a bowl, with a mixer on high speed, beat remaining 1 cup cream and the crème fraîche (see notes) until mixture holds medium-soft peaks. Stir about 1 cup cream mixture into caramel until no white streaks remain. Gently fold remaining cream mixture into caramel. When completely incorporated, whisk gently to thicken to spreadable consistency, if necessary. Use immediately, or cover and chill up to 3 hours.