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.
Gallois has played under many famous conductors, including Leonard Bernstein, Karl Böhm, Pierre Boulez, Sergiu Celibidache, Eugen Jochum, and Seiji Ozawa.
He also regularly collaborates in chamber music with Yuri Bashmet, Jörg Demus, Natalia Gutman, the Lindsay String Quartet, and Peter Schreier.