Mix the cream, eggs, white sugar, cinnamon and vanilla together very well in a very large bowl.
Slice the baguettes lengthwise then cut into 1" pieces.
Soak the bread in the cream mixture in the refrigerator overnight, covered.
Spray a 9x13 casserole dish with pan spray or coat with butter.
Layer in the soaked bread but not all the cream mixture. Discard the remaining cream mixture.
Leave the bread about 1/2" from the top so it has room to rise when baking.
Cover the top with brown sugar and bake at 325 for 45 minutes, then start checking and remove when center is set.