To obtain two parallel curves in illustrator, in the sense of a design shape you can work with, the most simple function is the "OBJECT>PATH>OFFSET PATH..." function.
You select the object you want to offset, than you set the parameters
The Object>Path>Offset Path function and way to find it.
The " Offset Path parameters"
The "Offset Path..." in action
...and the application (here the ZIP file). See the page it belongs too!
By the way, this is a typical Art Nouveau design, but it's origin is much more antique. The "palm leaf" decoration has Greek and Mycenean origins.
Below is a Walter Crane decoration from his book, "Form and Line (1900)", a collection of lessons he gave at the Manchester Municipality Art School when he was Director for the Design section.