The fragment of the Francos is one of the fragments of Dark Monk's key. It was being held by Roger de la Fontaine, the burgermaster of the Francos. Roger kept the fragment safe and hidden, without telling anyone where. One day, he was eaten by a gas monster, so the fragment got lost. As a result, everyone in the island begun searching for the lost fragment.
To find the fragment, Twinsen needs to find the Burgermaster's notes of where the fragment is hidden, and dig in the correct place with the pick-ax.