Like Caine said - this is more of a bread pudding than a "french toast". Soaking overnight in the batter will not cause it to fall apart - but how you cook it will affect how, or if, it browns. Had you removed it from the batter and cooked on a hot buttered grill or in a cast iron skillet (or non-stick sklllet) it would have turned nice and brown, and the proteins in the batter would have firmed up the bread.
"Stuffed" french toast is basically - wait ... we just discussed this! Golly but I love the little "SEARCH" button at the top of the page ... you might start with this thread
for ideas ...