Where is it broken?  There will be a difference between a non-structural point and part that needs strength e.g. supporting a hinge.   How large is the area needing repair?  How deep?
You say it is black.  Presumably that is lacquer?  What colour is it below the broken bit?

It seems strange that it is papier mâché if it broke so easily into pieces.  PM is usually very strong and not brittle, though that depends on age and the type of paper and adhesive used. 

What to do?  Oh gosh . . difficult without seeing it but thanks for such a careful description.
You could firstly see what you can put together, using either PVA (white glue) or spirit glue.  Use it sparingly and immediately wipe off any that appears on the surface.  If you have all the pieces, this might be enough.

If you need to do any filling-in you could try different methods.  One would be a small mix of a wall filler (e.g. Polyfilla in UK), mixed with a strong black powder (i.e. water-based) pigment.  If you have any worries about the mix sticking to the surrounding area, paint a very thin film of PVA in the hole first.

Another, for larger areas would be to take some toilet paper, soak it, squeeze it hard, mash it with a bit of PVA or thick wallpaper paste and black pigment until it is really malleable.   Pull off small bits and press them into the cavities, smoothing off while it is still moist.  Allow to dry thoroughly.

Finishing off with a coat of water based varnish will unify it all and make it sparkle again.

I hope someone else adds their ideas - the more thinking caps the better!

Thank you both for your helpful and considerate comments. I am amazed that anyone can be prepared to spend time like this over someone elses problem, much appreciated.

Yes, it is certainly old! I was told it is papier mache when I took it to a local antique expert, and I can sort of see that from the weight perhaps and feel of the material, also looking at pictures of similar things on the Web. I used to make thing in papier mache when I was little, made from newspaper and paste, but this is very different material it seems to me.

I am going to get together the materials you both suggest and try and make a start just to assemble everything and see if some the large pieces will indeed fix back as you suggest reasonably well onto the body of the box, and hopefully I will get a feel for the work then better.

I will try and post some pics!!

Thanks