Typing accented character changes font

I want to type an accented e character (é). I do this by first typing the Option+e key and then the e key again. This works most of the time. Today I've noticed however a problem with one of my fonts while working in Illustrator. It's 'EuroComic'. When I then want to add an é character by pressing Option+e and e again, when I've pressed Option-e the font changes to Myriad Pro and upon pressing e again I get the é character but in Myriad Pro. Tried it in TextEdit with the same font. Then when I press Option-e, the font changes from EuroComic to Lucinda. Haven't checked other fonts yet, but how is this possible?