What an interesting way to approach the theme of this book! I would say there are two ways you could broach the subject: by focusing on the movement of ignorance toward knowledge or by focusing on the movement of loneliness toward fulfillment. Both of these themes can and should be applied to the characters of Reneé and Paloma; however, I will fully analyze Reneé in regard to the first theme and Paloma in regard to the second in order to give you some wiggle room in your assignment.
The first idea of movement and theme would be that of "ignorance into knowledge." Renee moves from one to the other in quite a literal way. She hasn't had a lot of formal education (unlike many of the tenants in her building), so she schools herself by reading the classics. Even Mr. Ozu realizes fairly early on that she has named her cat Leo after Tolstoy. But there is a deeper level that Reneé touches upon as well. At the beginning, Reneé is confined by her stuffy French society.
[Reneé] has the elegance of the hedgehog: on the outside, she’s covered in quills [but on the inside] she has the same simple refinement as the hedgehog; a deceptively indolent little creature, fiercely solitary—and terribly elegant.
As a member of the lower class, she refuses to believe she could be friends with the educated Mr. Ozu. It is ignorance to believe so, as long as the person clings to nonconformity! Mr. Ozu himself helps her realize this:
You are not your sister, we can be friends. We can be anything we want to be.
In this way, Reneé comes from ignorance to knowledge. This excites Reneé, and she truly comes into her own by the end of the novel.
In regard to Paloma, it's really neat to look at the theme of movement from loneliness to fulfilling closeness. Here is a rich child who is so smart and so lonely that she has decided to burn down the building and kill herself when she turns thirteen! She writes philosophy like a pro and, at the beginning of the novel, nicely echoes Reneé's ideas in her diary entries. At this point Paloma and Reneé have not found each other. The irony is that it takes the catalyst, the Japanese Mr. Ozu, to bring the two soulmates together. This destroys all sorts of antagonistic cultural barriers: young/old, rich/poor, concierge/tenant, French/Japanese, etc. Through the catalyst of Mr. Ozu, Paloma finds fulfilling closeness with Reneé. Reneé even allows her to hide out when Paloma is fleeing from the superficiality of her own family. Reneé and Paloma begin to share their philosophies and find a soul connection with each other. It is simply not what society would expect.
Then the ultimate irony is that, because Reneé gives her life to help someone poorer than herself at the end of the book, that action and her previous relationships allow both Mr. Ozu and especially Paloma to move from death into life. Talk about the theme of movement! How about that one: death into life! This is nicely concluded by Paloma's words and the words of eNotes:
“How can you have a profound thought when your kindred soul is lying in a hospital refrigerator?” Paloma decides she will not commit suicide or burn the building down. Instead, because of Reneé, she will live on, "searching for those moments of always within never.”