The only thing he needed was the key. The original key had been lost in the fire, and all the other keys he found around the station and in the windup toys from the booth didn’t fit. But when he saw the key around Isabelle’s neck, he knew right away it would work. And now he had it. (1. 12.2)
Well, well, well. It's the final piece of the puzzle folks—the key that unlocks the mystery of the automaton, of Georges's past, of Hugo's future.
Hugo's done all the work that he can fixing that automaton, but he still needs something to fit into the mechanical man’s back. And isn't it odd that he can’t find that piece himself? How strange that he needs to use something that Isabelle has in order to get it started. Verrry interesting, no?
The thing is, the story stresses that it’s good to be independent, to have your own interests and your own brand of confidence, but sometimes you just need a little bit of help. You can be almost there, but a bit of human connection never hurts.
And for Hugo, he was able to fix the automaton all by himself, but he needed something that Isabelle had in order to get the contraption working. Otherwise, it's just a lifeless toy. With the key, it comes to life and brings them all together. That’s exactly what we’d call magic.