BB cartridge spindle ?
Is the spindle in a cartridge bottom bracket removable? It'd be cheaper for me to buy a whole cartridge style bb and use just the spindle than to buy a spindle on it's own. The reason I don't use the cartridge is cause I've got an old french bike and already have the french threaded cups.
As a rule, no they aren't removable since the entire unit is sealed. Even if you could get it out, the bearing surfaces wouldn't match cup-and-cone cups and loose bearings.
Phil Wood ($$$) offers their cartridge bearing bb's with French threads.
You can (maybe) order a replacement spindle for your old cup and cone BB. Maybe. Try Loose screws or Bike tools etc.