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.

Yes, 'juste comme' functions in the same way as 'just as' does in English. Despite Kwiziq marking me down for using it in the place of 'ainsi que' (in a 'just as' scenario), it works. But you cannot use it interchangeably with 'ainsi que', given that 'ainsi que' has other uses beyond 'just as'. For example, 'ainsi que' also means 'along with' or 'including'.