Just as - temporal, at the same time (as) - au moment où or juste quand / en même temps que 

Just as - in the same way/manner (as) - de la même façon/manière (que)

“Juste comme ça” - just like that.

For ainsi que I think of "as well as" coming close to its French meaning. So juste comme isn't quite there, in my understanding. And ainsi que is nicer French anyway. I love it when I can just drop it in a conversation.