  We study the symplectic leaves of the subvariety of fixed points of an
automorphism of a Calogero-Moser space induced by an element of finite order of
the normalizer of the associated complex reflection group $W$. We give a
parametrization {\it \`a la Harish-Chandra} of its symplectic leaves
(generalizing earlier works of Bellamy and Losev). This result is inspired by
the mysterious relations between the geometry of Calogero-Moser spaces and
unipotent representations of finite reductive groups, which will be the theme
of a forthcoming paper.
