Amélie visits her father, Raphaël Poulain, every week via train for some of the most miserable father-daughter lunches we've ever seen. It seems like he's been cold and distant since his wife died, but actually he's always been that way. Our first description of this dude, an ex-army doctor, is "tight lips, hard heart," and when Amélie asks him later how he would feel if someone found a "precious relic from [his] childhood," he says that nothing like that exists. We have to wonder if he ever had a childhood, or if he was born a full-grown grumpy man.
Still, he's her father, and even if he's never been affectionate, Amélie wants him to live a full life. Instead of moping around the house, tending to his dead wife's shrine and painting his garden gnome, Amélie thinks he should travel. But he's stuck.
So Amélie steals the gnome and turns her dad's life into a real-world Travelocity commercial, having her flight attendant friend mail the old coot photos of the gnome around the globe. This serves as a way for Amélie to both jab at her father and to inspire him to do some traveling of his own. In the end, it works.
Amélie's mother, Amandine, died when Amélie was a girl. A suicide jumper fell on top of her, which killed her (and the jumper). Raphaël built a shrine in the yard in Amandine's honor, but Amélie doesn't ever seem to miss her at all.
Like Amélie and Nino, Raphaël and his dead wife seem to have been soulmates. They're not fun and whimsical like Amélie and Nino, though; Raphaël and Amandine are both cranky, cold, and very, very particular. Amandine was a shaky-nerved schoolmistress who liked "figure skaters' costumes on TV, polishing the parquet, [and] emptying her handbag, cleaning it out, and putting everything back." This lines up with her husband's interests, which include "peeling large strips of wallpaper, lining up and shining his shoes, emptying his toolbox, cleaning it out, and putting everything back."
Very, very boring. It's almost as if these two people are so scared of life that they have to compulsively organize and clean everything, all the time in order to keep life at bay. Amélie's sheer creativity must come out of a need to rebel against this mind-numbing existence.