Cube the cheddar cheeses and pulse them in a food processor until crumbled.
Add the cubed brie (rind removed) and the white wine. Pulse until combined but not packed tightly.
Transfer the cheese into a medium bowl and set aside.
In another medium bowl, stir together the softened butter, honey and Dijon mustard until combined.
Butter one side of each slice of bread.
Place 6 slices of bread, butter side down on a working surface.
Divide and spread the cheese evenly among the 6 slices of bread.
Top the cheese of each sandwich evenly with the French fried onions.
Place the remaining buttered bread, butter side up, on top of each sandwich.
Preheat a large skillet on a medium heat.
Place 2 sandwiches in the skillet and cook on the first side until golden and the cheese is just beginning to melt.
Use a spatula to flip the sandwiches, cover if needed (to completely melt the cheese) and continue cooking on the other side until golden.
Cut in half, and serve hot.