My Dad thought everything should have a pad. A big, ugly, white line pad. I don’t know why.
That gun is a 12, short of 6 1/2 lbs. I can visualize somebody complaining about recoil easily enough, and thinking a pad would help. I’ve not noticed that pads help with recoil all that much, for sure not as much as wisely choosing the load used in the gun. But, as the OP noticed, the gun fits him, and I would bet the stock was not too much longer when it was new, and the cut was just to get a flat surface for the pad. None of them, are long stocked, compared to current production guns. It is a pre war French gun. Short is common.
That gun has not been used very hard. But, it isn’t a museum piece, either, and a day afield would sure be enjoyable with it.