Gallois was born in Linselles near the town of Lille in the north of France. At the age of 17 he began studies at the Conservatoire de Paris with the celebrated flutist Jean-Pierre Rampal and after two years received the First Prize. At the age of 21 he became principal flutist of the Orchestre National de France under Lorin Maazel. He served in that capacity from 1977 to 1984. In 1984 he left this post for a career as a flute soloist and, later, conductor.