The reason Amélie has such a hard time approaching Nino is not just that Amélie "doesn't relate to other people" and "was always a lonely child"--though that is part of it.
At the beginning of the movie, we learn a deeper reason: "Deprived of playmates, slung between a neurotic and an iceberg, Amelie retreats into her imagination."
She has, since childhood, sought not only solitude but solitude in an imaginary world. As far as other people in particular go, she "would rather imagine herself relating to an absent person than build relationships with those around her." The reason is that it is only in her private, make-believe world that Amélie feels completely at home, and perfectly safe.
To approach Nino directly, to see if they are compatible--this, a narrator explains, would be a reality-check. "The last thing Amélie wants." To pursue a relationship with him would demand that she place primary emphasis on her own life rather than fixing the lives of others. And it would also require of Amélie a virtue she presently lacks: courage.
As the movie nears its intellectual (and actual) climax, we see each of these issues come to the forefront.
Amélie is watching a foreign film on TV, with the subtitles supplied by her imagination (which here, allows us to see inside her mind at a crucial moment).
Dufayel, her house-bound neighbor, has previously pointed out Amélie's own messy life, and asked her who will fix that (while she's out working on the lives of others)--then, right before this scene, he points out that she doesn't approach the man she loves because she is in fact a coward.
On the TV screen, a guy "says" that "Dufayel's attempts to meddle are intolerable!" This gets a nod of agreement from Amélie. But then he goes on: "If Amelie chooses to live in a dream...and remain an introverted young woman...she has an absolute right to mess up her own life!" And to this, Amélie's eyes close, and her head lowers slightly in thought.
At this moment, Amélie has to weigh a handful of profoundly philosophical issues: to deal with reality, as it is, or to attempt to evade it; to place primary emphasis on her own life, or on the lives of others; to have the courage to pursue a relationship with the person she loves, despite being extremely shy, or to remain a coward--and a lonely one at that.
The choice Amélie makes will determine the course of her life--and of the film. Which choice will she make? Read on.