  In the centre of mass frame, we have studied theoretically the $Z$-boson
resonant production in the presence of an intense laser field via the weak
process $e^+e^- \to \mu^+\mu^-$. Dressing the incident particles by a
Circularly Polarized laser field (CP-laser field), at the first step, shows
that for a given laser field's parameters, the $Z$- boson cross section
decreases by several orders of magnitude. We have compared the the Total Cross
Section (TCS) obtained by using the scattering matrix method with that given by
the Breit-Wigner approach in the presence of a CP-laser field and the results
are found to be very consistent. This result indicates that Breit-Wigner
formula is valid not only for the laser-free process but also in the presence
of a CP-laser field. The dependence of the laser-assisted differential cross
section on the Centre of Mass Energy (CME) for different scattering angles
proves that it reaches its maximum for small and high scattering angles. At the
next step and by dressing both incident and scattered particles, we have shown
that the CP-laser field largely affects the TCS, especially when its strength
reaches $10^{9}\,V.cm^{-1}$. This result confirms that obtained for the elastic
electron-proton scattering in the presence of a CP-laser field [I. Dahiri et
al., arXiv:2102.00722v1]. It is interpreted by the fact that heavy interacting
particles require high laser field's intensity to affect the collision's cross
section.
