What you can say for sure is if those figs HAVE BEEN pollinated. Take a ripe fig, extract the seeds in a glass with water (you may need a few hours before the flesh separates) and check if they sink.
Let’s say the figs came from the main crop (not breba).
1. If the majority of the seeds is on the bottom and not flowing on the water's surface, the fig was pollinated.
As far as to say if that variety is a Smyrna type (assuming the fig you found is edible and not a capri) or a Common, I would still say you cannot tell since all the fig varieties could be pollinated.
2. On the other hand, if all the seeds float and the tree is covered in ripe figs, that var doesn’t require pollination, it is a Common type.
The middle ground is covered by the San Pedro types where the main crop needs to be pollinated and breba does not.