It is 32 bit.
I'm using Snow Leopard for this. Open System Profiler. Click on Applications under the Software tab. When the list finally returns, it takes time, scroll down to Final Cut Express. Click on that line and look at the far right column. Do you see 'No' under the 64-bit(Intel) column?
A rewrite of Final Cut Pro is expected to be released in the future that is 64 bit. At that time or likely sometime later, one would think Apple will release a new version of Final Cut Express based on that new rewrite.