It's been about 15 years since I saw the movie and cannot remember a thing about it, other than that it was colorful. So, for me, the musical version had to succeed on its own merits, divorced from its film predecessor. And in that regards, Amelie failed. Woefully.
Things didn't start out badly. The first 15 minutes or so have a certain Matilda-esque quality to them, with a singing goldfish, an inflatable tourist falling from Notre Dame, etc. But even then there were a few troubling things. Like: Why did one of the nuns at Notre Dame suddenly appear with an alligator's head? Did I miss something? Despite weird details like that, I was enjoying the show so far.
Then Amelie grows up, becomes Phillipa Soo, and moves to Paris. And the show begins its long, slow descent into mediocrity. Now, I don't mean to make it sound like Soo is the issue here. She's not. She acts bright & chipper, and sings fine. It's just that the story becomes increasingly muddled, with undeveloped subplots and characters, all served up with forced helpings of whimsy.
We are told, for example, that Amelie has basically spent the past 5 years working at a cafe and watching people out her apartment window at night. (Why? She doesn't otherwise appear socially inept or awkward. Did I miss something again?)
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One night, as a result of Princess Diana dying(!), Amelie discovers a small box hidden under her apartment floor. She spends the next several scenes & songs trying to track down the box's owner. Suddenly, we are presented with a scene of her placing the box at a public phone and then luring the box's owner by ringing the phone. Because of this miraculous rediscovery from his childhood, said box owner suddenly calls his estranged wife(?) and asks to see his child. (Huh? Who? What? Did I miss something again?)
I bring this up because we have not seen this character before! (I believe he was in the opening number as a child, but that's it.) We have absolutely no connection to him or his story. We don't even know how Amelie eventually found him and set up the phone gag once she learned his name. Character & situation & resolution all come out of the blue.
And so it goes. On & on. We get strange stuff like an Elton John number (prompted by Princess Di's funeral) and the Travelocity Gnome going on a trip around the world (with a stewardess who barely exists as a character at all). But none of it really connects up and, so, none of it really matters. Unless, I suppose, one can relate all this to the movie version and are content to see it referenced on stage.
Then, as the musical continues to circle the drain, we get the most protracted denouement imaginable. It seems like the last half hour is spent with scene after scene and song after song of Amelie and Nino chasing and dodging each other around Paris. LOTS of fidgeting going on in the audience by this point; the lady next to me actually fell asleep. (By the way, why does Amelie wear a nun's habit to the porn shop? Did I miss something again?)
As others have said, the music is incredibly monotonous, with number after number sounding exactly the same. I think adding book scenes could actually help this show quite a bit. As it is, it's just a relatively inoffensive, occasionally engaging, frustratingly underdeveloped mess.
It sure was colorful, though.