The first and third part work so well because the characters are so sympathetic, we watch them believably transform from amiably superfical loafers to genuinely loving adults. This transformation is believable because the raw material was pretty good to begin with: Michel might seem almost intolerably playboy material, the archetypal French lover that only exists in non-French imaginations, all corny lines and cynical intention, but the trip to the grandmother's suggests his true value.
However, he needs more life lessons than Terry. Maybe this is because Irene Dunne's persona, in films like 'Cimarron' or 'Show Boat', was based on moral transformation, on the difficult negotiation of the road to adulthood through life. Charles Boyer, well, he's French, isn't he? So whereas Terry is completely transformed by the visit, Michel has more difficulty in letting go of his ego. Terry's failure to meet the appointment is a personal affront: he never once asks why she mightn't have made it. Because he is French, and a playboy, he is cynical about women and their motives, can't take anything on trust. This is what makes the final scene so truly moving - two lovers who really need to be together are reunited, yes, but also, Michel finally comes to full moral awareness, full maturity.
It is, ironically, his own painting that reveals the truth to him (his artform in her territory). The romance narrative is framed in terms of art: Michel is a failed/abandoned painter and poet; Terry is a singer - the transformation scene occurs over the grandmother's piano player (her artform on his territory). The couple meet again at the theatre.
This is part of a wider dialectic about public roles and private desire. The film opens with various global radio gossips announcing Michel's engagement: his personal life is conducted in public, complete with groupies, autographs, paparazzi. His developing relationship with Terry is similarly framed, the audience on the boat eagerly watching it like a soap opera.
The first appeal of the grandmother's house is its quiet, its distance from the world. It is also the place we first learn that the protagonists are artists. it is at this point they begin the inexorable, but slow and obstacle-laden, road from public to private, from an agog dancing hall to a solitary apartment. Art helps them express their personal essences apart from their public reputations, but it also must go through the public mart before it can express private truths - Terry becomes a nightclub singer, then an orphanage instructor; Michel paints on billboards, than for clients.
It is only when art is made private - when Terry accompanies the grandmother; when Michel sees his painting in Terry's bedroom - that is truths are revealed. This last revelation is brilliantly framed by McCarey: we see the painting in a mirror, continuing a visual and structural pattern leading the heroes to self-awareness.
For me, the film is moving for another reason. The grandmother scene is obviously the crucial one. Although we first meet her in a chapel, she is more like a witch, or fairy godmother, her home an enchanted realm. It is her mischievous suggestion that breaks both friends' pre-destined course: after her purpose is achieved, she vanishes. Waiting to die to return to her husband, we are reminded of Charles Boyer's biography and are doubly moved.
But there's more. Both Terry and Michel seem equally lightweight until this visit, but immediately we see Michel connected to a culture, a family, a religion that goes back centuries, that has seemingly unbreakable roots, while Terry, an American, has 'nothing' but a wise drunken father. This is a central stop of a trip from Europe to America; here Terry acquires European culture, a depth her own country doesn't have.
This is one reason the piano sequence is so powerful. But there's another. Although the film never mentions events in Europe, we don't have to look too hard in this tale of a rich European intellectual doing menial work in the States, in this film full of refugees and travel: when the cultured widow of a French diplomat dies in 1939, we are losing more than an old woman.