What do you call a fence around a balcony?

That’s called a ​balustrade​ or, more commonly, a ​railing.

Here’s a more detailed breakdown:

• ​Balustrade:​​ This is the formal architectural term for the entire structure—the railing system that includes the supporting posts and the top rail.
• ​Balusters:​​ These are the individual, often decorative, vertical posts or spindles that hold up the top rail.
• ​Railing:​​ This is the most common and widely understood term for everyday conversation. It refers to the protective barrier itself.
• ​Handrail:​​ This specifically refers to the top part of the balustrade that you can grip.

In some contexts, especially with older or solid-walled structures, it might be called a ​parapet.

So, for most purposes, you can simply call it a ​balcony railing.