Unfortunately, the older Express cannot be used to "extend a wireless network" since it does not have the settings to do this.
And....if you try to configure the new AirPort Express to operate in WDS mode, you throw most of the performance capability of the new Express out the window.
For example, WDS will only operate in "g" wireless mode, so you lose all of the faster "n" capability of the new Express.
Even worse, WDS cuts the bandwidth on the entire network in half....so if you setup a WDS arrangement....you will have an older "g" wireless network running at half speed. Definitely not recommended.
On top of that....WDS is very difficult for most users to set up correctly. To get an idea of the challenge, look over this Apple support document:
My suggestion would be to swallow hard and upgrade your network. Get another new AirPort Express and you will have a first rate network. The Ethernet port on the Express is automatically enabled when it is configured to "Extend a wireless network".