I have read about 'Orgue de Barbarie', but about the name of
various fair organs, many people in France say only "Oh! A Limonaire!"
The name Limonaire is, for example, like saying Hoover for a vacuum
cleaner in England.

But Alain Vian (brother of the French poet Boris Vian) was a specialised
mechanical music instruments tradesman, and at this question about the
name Limonaire, he gave this answer:

  "A very old maker of fair organs had made a very nice organ,
   and when he started to play the first punched card, he said,
  'Lis mon air (Read my melody)'!"

It is a joke, because "Limonaire" and "Lis mon air" sound alike in
French!  But Alain Vian had plenty of humor...

Best regards from Mirecourt
Francoise Dussour