I took a little time to think how best to respond here. With the proviso that I’m no expert on watches, I have a few comments.
The dial is signed “Deroches AGENEVE” (ie Deroches of Geneva, Switzerland) but the movement is signed “Breguet à Paris”. Might a Deroches dial be fitted to a Breguet movement? It’s possible, but I’m doubtful. Also compare your rather untidy signature on the left to the beautifully executed one on the right.
If it were a genuine Breguet movement, it would have to be late 18th Century. The Breguet workshop was founded in Paris by Abraham-Louis Breguet in 1775 and quickly became a supplier to aristocracy and then royalty. He worked on his own as a master craftsman, apart from a short-lived partnership with Xavier Gide between 1787-1791, and returned to his native Switzerland in 1793 when things turned ugly in Paris during the French Revolution. He then worked out of Geneva and didn’t return to Paris to begin re-establishing his business until 1795.
According to the authenticators at the Breguet business (it still exists), any
19th-century pocket watch bearing the signature “Breguet à Paris” is fake. They also say that none of the watches bearing the words “Spiral Breguet” were made by Breguet and that any pocket watch with an individual serial number higher than 5500 is also fake. [Note that this does not refer to the ‘55326’ number on the case for your watch. Your case was made by someone else but I can’t read the mark in your picture apart from the letters at the bottom, which look like ‘AL’]. In any case, around 1807 Abraham-Louis Breguet took on his son Louis-Antoine as his partner, renaming the firm "Breguet
et Fils" (Breguet and Sons).
Breguet watches were the Rolex of their day and suffered the same problem. They were widely faked by Eastern European manufacturers… especially in the 19th Century and up to about 1910… to the extent that fakes are considerably more numerous than the real thing.
Note that in the example Don linked to, both the dial
and the movement are signed “Fres Deroches A.GENEVE” (ie Deroches
Brothers of Geneva, and not just “Deroches”). The typeface styling is also very different and I think this is not the same ‘Deroches’ as for your watch. I've superimposed the marks onto your watch for comparison:
There were at least eight (unconnected) companies making watches in Geneva and using the name “Deroches” during the late 1700s to mid 1800s and I wouldn’t like to say which of them relates to your watch, or what date it might actually be... but I'm leaning towards a 19th Century inferior imitation.