Often with French wired lamps, the cord is glued or attached to the side of the base, so that it follows the contour of the lamp base. This is somewhat acceptable for some bases, especially if they are carved in such a way that there is a groove that the wire can fit into, but for many bases this does not work. Alternatively, you might be able to have the lamp rewired, providing the base is either hollow or has a wireway.

What is the base made of, and how does it look?

Thank you so much for your reply!

The base is made of solid crystal.

Here is a link that might be useful: restoration hardware