It went by in conversation that Etienne is French for Stephen. I never knew that, but it clicked in immediately that this was a pattern. Ecole = School, etranger = stranger, etat = state. There also seem to be a lot of English words where both versions have come down, presumably the earlier version from the Germanic languages, plus a newer version from Norman French. State, estate; scapegoat, escape; stay (stand, stable), establish.
This is where search engines become my favorite thing. Until just a few years ago, that is as far as my thought would have gone. I would have to either go to a library and thumb through a dozen linguistics books, or wait until I met someone who was a trained linguist or was familiar with French word etymology or Old French. Now I just search. Amazing.
The adding on of the /e/ to the Latin forms that had only the /s/ beginning happened in both Old French and Old Spanish (states, estados). This is called prothesis. So Old French for "state" would have been estat. The dropped /s/ is called a syncope. My guesses about Germanic roots and Norman French acquisitions was correct.