Character classes are formed at regex compile-time, and \1 isn't a backreference until regex run-time, so your character class is saying "all characters except the character with octal code 001". Try something like:
in reply to Mind boggling regex
which reads "match an e, then, making sure we CAN'T match an e, match ANY character, then match an e." The /s is there so that . matches newline.
$word =~ /(e)(?!\1)(.)e/s;