If you are going to do anything to the finish including stripping it then you should start with a wax and grease remover to rid the box of as much furniture polish as you can. The waxes and polishes used on the box over the years will give you a lot of trouble refinishing it.
If the piece has sentimental value I think the less you do to it the better. You might put a drop of lacquer thinner on it in an inconspicuous place and see what happens. I think the finish on it now is probably lacquer. If it is then much of the spots will go away if recoated with lacquer.
If you are going to actually refinish it then start with paint and varnish remover. Sanding a finish off is really only good on metal. With wood part of the finish penetrates into the wood and if you sand it off there may be places the wood is still sealed. You can't see these places until you stain and it goes on blotchy.
If you are going to refinish the metal rosettes will need to be removed that will probably be very close to impossible without damaging them. You might use a utility knife blade with a pair of vice grips to get under them. After getting them off I wouldn't do any more than maybe rub them with some 0000 steel wool. The wait until you are almost done with the French Polish and re-apply them.
Brushing linseed oil on after using the alcohol stain won't provide a barrier coat when wiping the shellac. Shellac is very difficult to apply by hand. If that is what you wish to use I would spray it. If you don't have spray equipment shellac is available in rattle can. From there you could do the French Polish but spraying the finish you might find out that isn't necessary.