Merci Marina, c'est intéressant ! In that case it possibly is an older type of building - I agree, 'flat opposite' fits any situation and also allows for 'palier', whatever is meant by that.

Whatever you prefer. 'opposite flat' is vague enough to suit any case.
The only problem is that unique sentence with 'palier' which can't be used for a courtyard.
In modern buildings I've never seen windows facing the stairwell area. In old ones with wide stairwell areas and room for a few plants, bicycles, prams at the bottom you will find some.

In the previous chapter un Unit 79 in response to the question: where did you meet her? Alexandre replies: Sur le palier... Elle habitait l’appartement d’en face. On the landing. I assumed that meant an enclosed building with a couple of apartments on each floor, where there aren't typically any windows facing outward into the stairwell area.
In the next unit however, she talks about seeing him through the window. So now I think that it is probably an apartment complex with some kind of courtyard in the middle as France previously suggested, where the apartments do have windows facing into the courtyard - and that is why she is able to see into his apartment.
I would probably translate this sentence as: Alexandre - You've been living in the opposite flat for several weeks . . . Why now?