[10] The municipality (originally the parish) is named after the old Foldereid farm (Old Norse: Foldareið).

The first element is the genitive case of the name of the local fjord, fold, which has an uncertain meaning.

The last element is eið which means "isthmus", due to the fact that the Foldereid farm lies on a rather flat piece of land that is about 2 kilometres (1.2 mi) wide between the Foldafjorden and an arm of the Bindalsfjorden to the north.

At the time of the municipal dissolution, it was part of the Kolvereid prestegjeld and the Ytre Namdal prosti (deanery) in the Diocese of Nidaros.

The municipal council (Herredsstyre) of Foldereid was made up of 13 representatives that were elected to four year terms.