Bob,
Your gun IS a model 408.
Guessing, it may have been made in part to satisfy the French market as it has features common to many French guns [rib treatment, strap, reasonably light weight bbls. & overall weight]. It is a gun designed to be carried about much more than shot. Call it an Italian 'game gun', which it is.
The issue with the firing pin holes 'COULD' be from use w/ammo using 'soft' primers or with thin rims as easily as dry firing, though the latter is perhaps more probable. There is a LOT more variation in ammunition from a rim thickness perspective than gets general discussion. Skeetex has given you good advice.
BTW, your gun as I'm sure you already know is proved for standard loads, not the heavy stuff. I'd look into some of the 24 gram/ 7/8oz. or even 3/4oz. reloads using VP05 wads from Ballistic Products or the newer Clay Buster 3/4oz. wads & E3 or one of the other suitable powders for enjoying it to the fullest on clay targets and on dove or behind a dog on flushed birds. Shooting anything heavier than an ounce [28 grams] will only beat both you & the gun up if you plan to shoot it as lot, mostly YOU at that weight.
I'd hope that you get much enjoyment from using it.
