It was Bond’s declaration of love to Books. There they were in love and he would die. By saying it to the girl on the it’s sort of ambiguous. But she will tell about it and eventually Bond will hear and she will know the love was mutusl. Unless he was in for Lolitas …

I have watched this film a half a dozen times and always assumed it was "False spring". But I just now listened to it paying full atention after reading this thread, and Bond definitely says "FALL Spring" So does J.B. when talking to the girl in the trolley.

Yes the term is a False Spring, meaning some unseasonably warm weather in winter that might seem like spring had come very early. However it is only a temporary respite before the cold winter weather returns.
Also as he exits the trolley, Books says something to the girl like, I hope the right young man will come along for you.

There are innumerable references to "false spring" throughout Wikipedia and Google, but none to "fall spring".

No, it was false spring.

I believe what John Wayne and Mrs. Gillum said was that the day seemed " like a Fall Spring ". In other words it felt like a combination of a Fall (Autumn) and a Spring day.

I believe "False Spring" is specific to an unusually nice winter day (remember the dates are mentioned - early January as I recall).
This term might be a kissing-cousin to "Indian Summer", but I am only guessing.
"False Spring", from a weather standpoint, is a symbol for a dying man who summons his last energies to be vibrant.
That is who I view it..

It could also be a reference to spring being a time of renewal and new life. A "false spring" could be unfulfilled hope; it would be appropriate for Books, who knows he could have just arranged his own death.

Thank you for the info. I never could tell which way the line went when either Books or Bond said it.

He says: "It's what we call a false spring" the exact same line told to him by Bond during their last conversation.
I've always thought it was meant to join the characters of JB and Bond together. As he rides the trolley to what he thinks is almost certain death he is thinking of her.