Allow cheese to stand at room temperature for 20 to 30 minutes, which will help it melt more quickly and evenly.
Heat the broiler. Set the rack about 4 inches below the broiler.
Cut the crusts off the slices of bread. Cut each bread slice into 4 equal strips.
Wrap one bread strip halfway around one grape and poke a long metal skewer through the bread and grape so that the skewer is pushed through both ends of the bread strip with the grape in the middle. Repeat with remaining bread and grapes.
Place all 16 skewers on a large baking sheet. Broil for 2 to 3 minutes, or until the bread is browned and crisp, turning once halfway through broiling. Set aside,.
In a small saucepan, bring water and shallot to a simmer. Cook, uncovered, until the shallots are tender, about 2 minutes.
Meanwhile, in a small bowl, mix the arrowroot with one ounce of the champagne. Pour the remaining champagne into the saucepan with the shallot. Whisk the arrowroot and champagne mixture into the saucepan. Continue to cook and whisk until the mixture is thickened, about 30 seconds.
Reduce the heat to low and all the Jarlsberg, whisking constantly until the cheese is melted.
Add the pecorino and continue whisking until melted.
Repeat with the brie.
Season to taste with salt and a pinch of cayenne.
Pour the mixture into a fondue pot and serve with the skewered bread and grapes for dipping. (Or whatever else you like to dip in a cheese fondue).