"the total width of the nut is 4.2cm
from the middle of the 6th string to the middle of the first slot seems to be 3.8cm
I think!"

4.2 cm, or 42 mm, is 1-5/8" which is the same as my Strat's nut-width - a bit narrow for an acoustic guitar. The spec on Guitar.co.uk website says 43 mm, which is the more usual width for an acoustic guitar of 1-11/16", so I think your measurement might be a millimetre off.

That string-spread of 38 mm matches the spread on my Martin HD-28V which has a 43 mm (1-11/16") nut-width.

So the Paramount seems to have a bog-standard 43 mm nut and 38 mm spread.

I think! ;-)