Dear kaddar, here is a partial answer.

According to a theorem of Douady, a  flat map $f:X\to S$ between complex analytic spaces is always open . If you assume that your reduced space $S$ is actually smooth (i.e. is a manifold), then $X$ is indeed reduced : this follows from the Proposition on page 165 of Gerd Fischer's *Complex Analytic Geometry* 
(Springer, LNM 538, 1976).