Looks to be gold so possibly no model could be Dennison or shackman no idea unless you can open the back
There will be a case ref number so you can do some searches from this , to find similar dials ect
Girard do offer a historic check but when I last inquired about 3 or 4 years back now there is a charge for this service . I never bothered as info online suggests it's not that accurate, as records were lost due to various times the company was sold .
It's a lovely watch from a great maker I would definitely get it sorted .