This is a story that she has not told ever before.
She begins talking to him as if he was so.
Although we can see some parallelism between the two cities, Resnais ends up the film with a scene in which this relationship seems to be much stronger.
Personally, I felt somewhat frustrated the first time I saw it.
We cannot differentiate what she was feeling at the moment of the story or what she is feeling now, what is a fact and what is a memory.
Whatever way it might be, Resnais leaves for us a cryptic, dark ending that we would have to figure out the best we can depending on the elements he has given us in the film.
I find very interesting the scene in which they sit together at the bar: at some point she takes the Japanese man for her old love.
But an affair with a Japanese man while she shoots a film in Hiroshima will wake up her memories.