...you just call the same audio functions you did before? Like play()? If you're asking about variable scope, then just make a global variable for your game's music so you can change it from anywhere. If you know C++ that should go without saying.
You may have heard that global variables are evil, but for a little toy program like this it's fine. As you develop your game eventually you'll hit a point where the downsides of globals become annoying and it makes sense to put the global music object inside a class or something.
For the condition, that's also making it sound like you don't know C++. Obviously, the code under if(event.type == sf::Event::MouseButtonPressed) gets executed every time a mouse click happens, so if you have no condition at all, obviously the music changes every time you click. If you want it to change when the game is in the PLAY state and you click, then use an if(CurrentState == PLAY) statement. But since that music changing code stops the menu music and starts the play music, it looks like you intend it to be executed when the game switches to PLAY mode. Whatever you intend it to do, that's what you should write. I only asked about that line because it didn't appear to match what you said you wanted.