One way to determine the age is to put on your lt. Columbo hat on and find the original owners or a neighbour or someone who knew them who may remember when it was planted.
What climatic zone are you in?
Check to see if the tree has died back to the ground. If it has grown continuously, measure the width of the lower trunk you could get some idea how old the tree is by how thick the trunk.
Fig tree varieties do vary in grow habit but it seems to me 1" width per year should give you an idea on the age.