Carr was born in Downings in north-western County Donegal; his father was a fisherman, and he grew up speaking Irish.
When he was twelve, Carr won a scholarship to Scoil Éanna in County Galway, an Irish-language school specialising in preparing students for teacher training.
He then went to St Patrick's College of Education in Dublin, where he led an unofficial student social committee, organising dances and performances by bands – including Phil Lynott.
He also set up a poker club with Joe O'Toole, which was still running forty years later.
[1] In his spare time, he worked as a DJ, a job the Sunday World campaigned against as inappropriate for a principal.