The OED goes with the eggy version:
"any of various kinds of toasted bread, esp. bread soaked in seasoned beaten egg and fried until brown, typically eaten as a dish at breakfast or brunch"
However, looking at the earliest known usage of the term, I quite fancy it as it was back in 1660:
"French Toasts. Cut French Bread, and toast it in pretty thick toasts on a clean gridiron, and serve them steeped in claret, sack, or any wine, with sugar and juyce of orange".
Bristol's 'Western Daily Press' though favoured the simpler style in 1924:
"A piece of bread and butter toasted on the dry side is said to be French toast".