Born in Bischwiller, Muller started out in Alsace, his native region, and then made a name for himself with the Stade de Reims, that he was twice crowned French champion. He then moved to Real Madrid, where he appeared in the European Cup final in 1964; they won league three times. He would move to FC Barcelona. Although he was touted as the successor to Raymond Kopa, his performances in the French kit never matched his club performances. He was nevertheless part of the French team that participated in the 1966 FIFA World Cup. He returned to Reims where he ended his career.
He briefly returned to Barcelona as a coach in the late 1970s, leading the club to the European Cup Winners' Cup Final, before being replaced by Joaquim Rifé. He would later train AS Monaco, RCD Mallorca and CD Castellón.
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