Crochet was born in Paris, where she studied piano with Yvonne Lefébure and Nadia Boulanger at the Conservatoire de Paris. She also worked with Marcel Samuel-Rousseau, Pierre Pasquier, Pierre Petit, Norbert Dufourcq. In 1953, she won first prize at the Conservatoire. She continued her piano studies with Edwin Fischer and Rudolf Serkin. At the international competition in Geneva in 1956, she won the first prize, and was among the winners of the International Tchaikovsky Competition in Moscow in 1958. In Bern, Rudolf Serkin heard her playing and invited her to follow his masterclasses. Crochet accepted Serkin's offer, then moved to the United States in 1958. As a soloist, she has performed in numerous American and European concert halls, including the Carnegie Hall at New York, the Symphony Hall at Boston, the Symphony Center of Chicago, the Royal Festival Hall in London, the Concertgebouw at Amsterdam, and the Konzerthaus, Vienna. Crochet worked for many years with the Boston Symphony Orchestra, then with many other orchestras in Germany, among others, with the Bavarian Radio Symphony Orchestra and the NDR Radiophilharmonie. As a university professor, she has taught at various American universities (Brandeis, Rutgers, Boston, the Georgia State University) and the New England Conservatory of Music in Boston).