Robin wrote:
So where did Juliet balcony get it's name then?

Shakespeare.

Not in what he writ. There is no "balcony " in the texts. Juliet
appears at a "window".

(Even more) boring details follow:

I think a lots goes back to all the cheesy productions of Romeo and
Juliet in which Juliet poses around a (conventional) balcony and/or
Romeo shows
his prowess by hoisting himself over the overhang. There is also the
Casa di Giulietta in Verona with Juilet's (purported) balcony. The 2
scenes in the play are also known generally as the balcony scenes.
Hence
people think there must be a balcony.

I believe they are called French balcony.

I forgot to say before that I do agree that "French balcony" is (or
used to be) used for what TMH described. But I'd
rather thought that it had been displaced by "Juliet (or Juliettte)
balcony". Possibly 'cos estate agents think it sounds more alluring
for the explosion of flats with
windows of that ilk? And/or because the planning guidance refers to
'Juliet' balconies normally
being permitted development and not needing planning permission?

It could well be either now estate agents are involved. It sounds so much
better that safety fence which is in fact, what it is.

So Shakspeare did not have a balcony but I bet if you ask one hundred people
to name a scene from Romeo and Juliet they will say "balcony":-)

--
Adam