This article relies on two recent developments of well known methods which are a color Fourier transform using geometric algebra \cite{TMC} and Generalized Fourier descriptors defined from the group $M_2$ of the motion of the plane \cite{Fethi}. In this paper, new generalized color Fourier descriptors ($GCFD$) are proposed. They depend on the choice of a bivector $B$ acting as an analysis plane in a colorimetric space. The relevance of proposed descriptors is discussed on several color image databases. In particular, the influence of parameter $B$ is studied regarding the type of images. It appears that proposed descriptors are more compact with a lower complexity and better classification rate.