The FCC-ee phase of a Future Circular Collider is generating great interest due to its versatility, allowing the study of various electroweak thresholds: $Z$, $WW$, $ZH$, and $t \bar{t}$. Electroweak precision physics is complemented by flavour physics measurements based on the unprecedented statistics attainable at the $Z$ pole, and benefiting from the low-background experimental environment (similar to Belle II), and from the production of the full spectrum of hadron species together with large boosts (similar to LHCb). A wide range of measurements is possible, spanning a rich variety of physics cases in both quark and lepton flavour physics sectors. Other electroweak thresholds can also be considered in this endeavour. A commensurate effort from the theory community will be needed to interpret future measurements. I present an overview of the broad potential of the FCC-ee flavour physics program.