Hello, my friend. According to your trouble, I have two thoughts. The first one is going to check the free space on Macintosh HD or the external hard drive used to store the exported mov files. If the drive has insufficient space for the files to store, then you can't export mov files successfully. You can use iBoysoft DiskGeeker to clean storage on your machine.
The second one is to check if there is any update available on your device, including the updates to the Final Cut Express and to your machine operating system.