"Burke's Landed Gentry" 1852 edition, "Adair of Bellgrove" stated that the family descended from Thomas, 6th Earl of Desmond who m. dau of Wm. McCormick. He then fled to France. He had son Maurice fitzThomas Fitzgerald, the $64 question is, is Maurice the Fitzgerald de Adair who then went to Scotland ?
Gerald FitzMaurice FitzGerald, 3rd Earl of Desmond who acceded 1357 and died 1398 had 3 sons, the eldest was John fitzGerald, 4th Earl of Desmond & Earl of Decies,who had son Thomas fitzJohn FitzGerald 6th Earl of Desmond.
Thomas fitzJohn Fitzgerald, the 6th Earl of Desmond acceded 1401, deposed 1411 by James 7th Earl of Desmond, who was also Lord of Decies.(Thomas had married Catherine MacCormac and had son Maurice fitzThomas FitzGerald de Adair who may have gone over to Scotland).This seems to fit in with the "Adair of Bellgrove" entry in Burkes.