Planès was born in Lyon, France, in 1948. At age five he began playing the piano and at eight appeared in concert with an orchestra. Young Alain inherited his mother's love for the arts, divulging not only a prodigious keyboard talent but an affinity for poetry and painting. At 12 he won first prize in a competition at the Lyon Conservatory, then enrolled at the Paris Conservatory shortly afterward for studies with Jacques Février.
Planès engaged in further music study in the United States at the University of Indiana at Bloomington, where his most important teachers were Menahem Pressler, Franco Gulli, William Primrose, and György Sebök. Planès soon became a regular partner in chamber concerts of cello virtuoso Janos Starker. After his return to France, Planès served for a time as the pianist for Pierre Boulez's Ensemble InterContemporain. In 1981 he left this post to launch his international career as soloist and chamber player. Throughout the 1980s he built his reputation on a mixture of solo and chamber appearances, and soon his recordings began to draw notice as well. His initial effort for Harmonia Mundi was the 1991 collaboration with cellist Lluís Claret in cello sonatas by Chopin and Richard Strauss. A string of other recordings followed, including an eight-disc series of Schubert sonatas and solo works, as well as a substantial series of keyboard sonatas by Haydn. In the new century Planès remained busy as a soloist and chamber player, appearing with the leading orchestras and at many festivals, including Marlboro, Aix-en-Provence, and Montreux. His recordings include the 2006 CD of Debussy's Children's Corner Suite, and Chopin chez Pleyel, on a period instrument.