I am posting here in the hope that someone will be able and willing to help me find some information regarding this watch (and another, but I'll post that later).
Getting the macro shots for this was quite difficult - I only have a cheap point-and-shoot. Despite the macro being fairly useless, I managed to get some shots which I hope are acceptable. I managed to interpose a lens from a binocular between the camera, and that seemed to do the trick.
To summarise the information:
The dial is marked 'DuBois' in an italic script, with 'INCASSABLE' also present (which translates as 'unbreakable' and although it runs, 'unbreakable' might be optimistic ).
The movement is marked 'PH.DUBOIS & FILS' and 'LOCLE' and 'C.30'. These are all in a small, uniform, sans serif typeface. However the markings on the plate holding the regulator arm are in a copperplate typeface. It has a Côtes de Genève decoration, and there is anglage consistently applied to the plates. 'Unbreakable' probably refers to the jewelled bearing holding the balance staff - there appears to be a rudimentary shock protection system... although it might simply be holding the jewel in place - excuse my ignorance.
The case back is marked 'METAL CHROME', 'FOND ACIER', 'INOXYDABLE' and '55380'. There is also a diagram/emblem/maker's mark which shows three pine trees and the letters 'D.B F' (I thinks it's an F - it fits with Du Bois & Fils - although it does look more like a capital gamma). A perlage decoration is applied to the inside of the caseback. This watch is tiny - I know that contemporary watches are very large, so this opinion is perhaps malformed - but across the case between ten and four, it only measures 26.5mm (Vernier calipers). Nevertheless, it is very legible.
I have tried to do my due dilligence so I do not waste anyone's time, but I can find very little information about Du Bois & Fils. Currently it appears to be a resurrected brand, with all the puffery and suchlike that is associated with these companies. Of the original brand I have found very little. I would be most grateful if anyone could provide me with information about the movement, Du Bois & Fils and the watch in general - especially the movement (for my interest) and its likely age (for my Mother's interest).
Have a good weekend!