As far as I know the springs are the same - they are sold as 500/126 springs by suppliers.
If the spring is corroded it will need stripping down and cleaning up and the plastic dividers will probably need replacing. If the spring is badly corroded or pitted then its only a matter of time before it cracks in cold weather.
Check the bushes in the spring eyes - if the holes have become oval or the rubber looks perished then replace them as its essential they do their job.
Another thing that affects the whole geometry how the spring is fitted - it must be fitted under load, so before any bolts are tightened the car must be lowered off the jack and weighed down until the distance between the centre of the eyes and the underside of the spring at the far side of the nearest mount is about 28mm - hard to explain but see the drawing below. This aspect of fitting the spring seems to have been neglected by haynes in the 126 book but is covered in detail in the 500 one.

(This is Fiat 500 wheels and their pram tyres so ignore the other figures for 126s - the 28mm is correct for 126s)
Once the spring is under load you can tighten it all up and it should sit properly.
Finally, don't skimp on suspension - it can be deadly if its worn out. If you have used some old shock absorbers, plan to replace them as soon as you can afford it.