the Fulbright French ETA just pays for more (travel expenses, stipend, and other things etc.) and requires the side plan or research or whatever in addition to your teaching. and has the prestige of the title of Fulbright and is thus more competitive. The French Embassy Teaching Assistantship requires you to work 12 hours per week and gives you 800 ish Euro a month (which is enough or not depending on your placement which can be anywhere), they don't pay your travel expenses or anything else, and it's much much less competitive. it's essentially the same thing other than certain benefits and prestige though.