> Ecole is the first word I learned in French and to this day I forget is it's a grave or aigu.

What I've noticed with most French words is that initial-è seems to be phonotactically disfavored if not outright forbidden. A quick scan of my dictionary suggests the only word with initial-è is ès which is archaic. In general, I associate è with a sort of final position, using je préfère as the mnemonic (since it has both the accents in that conjugation).