Elsom was issued an international arrest warrant on charges relating to forgery, and misuse of corporate assets as reported by the Midi Olympique newspaper.
Elsom, 41, was president of Racing Club Narbonnais in 2015 and 2016 and left the club in a poor financial position which led to Narbonne's relegation to Federal 1.
The 75-test Wallaby is said to have embezzled nearly NZ$1.25 million during his time at RCN, for his own benefit and that of player friends.
He disappeared before his trial at the Narbonne Court.
Elsom recently announced that he was coaching at the Catholic University School in Ireland.