Plante was the eldest of 11 children. In 1949, he married Jacqueline Gagné; they had two sons, Michel and Richard. In 1970, Plante met his second wife, Raymonde Udrisard, with whom he eventually moved to Switzerland. He died in Geneva, on February 27, 1986, shortly after he had been diagnosed with untreatable stomach cancer. He was buried in Sierre.