the article

You've broken the sentence up incorrectly.




the brass rail was breast-high

____



the brass rail went around the most important table


____



the most important table in the private salon


____


There was a very high railing around the most important table in the private gambling room.

I'm not sure if this will help you, but listening to it might allow you to understand the phrase breaks more easily.

http://esl-bits.net/ESL.English.Learning.Audiobooks/Casino.Royale/01/default.html

Salle privée is French, it means private room. In the casino there was a special room for important rich customers.

In the private room the most important table is called the top table

Surrounding the top table is a brass rail which is breast high

Breast means chest. The rail was as high as a man's chest.

Other French words in that book:

http://commanderbond.net/1962/translations-royale.html

which surrounded breast-high the top table

which encircled at about the altitude of one's chest, the table which stood highest

"salle privée sounds like a private room.

That is the exact translation.