On 27 March 1977, Arconada played his first game for Spain, a 1–1 friendly with Hungary in Alicante, replacing Real Madrid's Miguel Ángel for the second half. Having captained the nation on many occasions, he represented it at the 1978 and 1982 FIFA World Cups as well as at UEFA Euro 1980 and 1984. In the latter competition, his blunder resulted in the opening goal for hosts France in a 0–2 final defeat: he appeared to have smothered a free kick from Michel Platini under his chest in a diving save, but he fumbled the ball, which slid off under his body and rolled slowly into the net; despite his reputation as a world-class goalkeeper, several years later he was still widely remembered for the error, known as "Arconada's goal" in Spain.