I am texting a friend who might be busy. So I text him ' leave a message when you are free'? Is that correct?
The scenario you present is so common that nuance plays very little, if any, role in it.
But let's say that you wanted to express the idea that you respect the other person's time; it is valuable and in great demand. In that case, "when you become free" or "when you have a free moment" might do. The phrase "when you're free" is a little too casual to express anything more than that you realize there may be some delay in the response.
Both your examples
When you are free
When you become free
are essentially the same, obviously your friend will be free when he becomes free.
Since it is a friend, you might use
When you have a moment
When you get a chance
When it is convenient
might be considered more polite/formal.