The metal-dependent Fdh's feature Mo or W at their active sites.  These active sites resemble the motif seen in DMSO reductase, with two molybdopterin cofactors bound to Mo/W in a bidentate fashion.  The fifth and sixth ligands are sulfide and either cysteinate or selenocysteinate.
The mechanism of action appears to involve 2e redox of the metal centers, induced by hydride transfer from formate and release of carbon dioxide:
In this scheme,  represents the four thiolate-like ligands provided by the two dithiolene cofactors, the molybdopterins.  The dithiolene and cysteinyl/selenocysteinyl ligands are redox-innocent.  In terms of the molecular details, the mechanism remains uncertain, despite numerous investigations.  Most mechanisms assume that formate does not coordinate to Mo/W, in contrast to typical Mo/W oxo-transferases (e.g., DMSO reductase). A popular mechanistic proposal entails transfer of H from formate to the Mo/W=S group.