Since you can't boot a FreeDOS install floppy on the target machine, you can make a disk image, and mount/use it with identical geometry in a virtual machine, and then install the OS in the virtual machine, by booting it from floppy and installing to the virtual HDD image. When done, clone the HDD image to the CF card.
The trick is, you still need to figure out what geometry your target computer wants to use on the CF card. Some CF card data sheets tell the geometry, but it usually is the simulated hardware CHS geometry such as 7750/16/63 for a 4GB card, which may or may not be translated by the BIOS with some algorithm to logical CHS geometry such as 968/128/63.
But the 386SX is likely so old that it can't do geometry translation, so most compatible CF cards would be max 500MB. It may detect or use larger cards incorrectly, or just hang when presented with a larger card. At least it did not hang, but be sure the CF card size and geometry is detected and set correctly.