Well I have played some excellent platformers that had no real enemies. Things like Knytt Stories, Seiklus, and the like. I'm thinking the best way to go about it as a platformer would have it puzzle based or metroid like (as in powerups give you access to more areas). I don't see why you couldn't combine the two either. If you decide to go for metroid style, the powerups would probably come in the form of the whisps you collect. Maybe not cheesy standard powerups like run and high jump, but logical ones, like limited floating (realize you're dead), or access to previously unknown areas (remember where something was, and thus the path opens for you). Actually, that last thing could be the entire game, in which you have levels that have a mystery revolving around the girl's past to solve, and once you solve it, she remembers another place that has another mystery, and thus gains access to a new level.
It just doesn't sound like you should have actual enemies you fight. Maybe game ending traps if you do something really stupid so as to keep a challenge, but not enemies. A game that focuses on it's atmosphere seems to be the way to go here.
Finally, I don't think you should scrap any big ideas at this point, like the guy who the girl saves. Honestly I can't tell too much of where that's going from the limited info you've given us, but that doesn't mean it can't be implemented or is bad. Of course, this is just my opinion, and you're talking to a whole board. I suggest you get more responses before you decide on anything for sure.