Hidalgo grew up in Normandy, where he started playing football. He was named after Mexican patriot Miguel Hidalgo y Costilla. He was champion of Normandie Juniors in 1952 with US Normande, before signing up to Le Havre's books for two seasons, later playing for Reims, with whom he played and scored a goal in the 1956 European Cup final 4–3 defeat by Real Madrid.
Under the wing of Rocher, who signed him for Monaco, he won two Ligue 1 titles and two national cup titles. Between 1964 and 1970, he presided the UNFP, a players' syndicate.
On March 27 1976, he was appointed national team coach, replacing Stefan Kovacs and during a time when France were having difficulty in major tournaments. Included in his side was Michel Platini, who helped the side turn a new page in their book and get back to winning ways. In the 1982 FIFA World Cup he got to the semi-finals, where he lost to the West German side on penalties. In 1984 he won the European Football Championship beating Spain.
After his victory, he passed the reins over to Henri Michel and got a job as the Technical Director, where he remained until 1986, afterwards choosing a managerial position at Marseille. He is considered an idol among the Marseille supporters. He strayed from the limelight after 1991, taking a sidelining role as a football pundit on Demain, c'est foot, a football show on TMC Monte Carlo.