To prepare the red berry sauce: Combine all the berries and sugar in a blender and puree until smooth. Strain the berry puree through a fine sieve, discarding the seeds, and into a small saucepan. Place the saucepan over medium-low heat and simmer for 2 minutes, stirring frequently. Remove from the heat and keep warm while preparing the French toast.
To prepare the French toast: Using a fork, beat the eggs in a 13x9 baking dish to blend. Place the slices of brioche in the eggs and let stand for 5 minutes, or until the eggs are absorbed, turning the brioche slices once.
Melt the butter on a heavy large griddle pan over medium heat. Add the brioche slices to the hot pan and cook for about 2 minutes per side, or until golden brown on the outside and heated through. Meanwhile, stir the sugar and cinnamon on a large plate; set aside. Immediately place the hot French toast in the cinnamon-sugar and turn to coat completely.
Divide the French toast among 4 serving plates. Top with a dollop of crème fraiche. Spoon the berry puree over the French toast. Scatter the fresh berries over and serve immediately.