  By the probabilistic coupling approach which combines a new refined basic
coupling with the synchronous coupling for L\'evy processes, we obtain explicit
exponential contraction rates in terms of the standard $L^1$-Wasserstein
distance for the following Langevin dynamic $(X_t,Y_t)_{t\ge0}$ of
McKean-Vlasov type on $\mathbb{R}^{2d}$:
\begin{equation*}\left\{\begin{array}{l} dX_t=Y_tdt,\\
dY_t=\left(b(X_t)+\displaystyle\int_{\mathbb{R}^d}\tilde{b}(X_t,z)\mu^X_t(dz)-\gamma
Y_t\right)dt+dL_t,\quad \mu^X_t={\rm Law}(X_t),\end{array}\right.
\end{equation*} where $\gamma>0$, $b:\mathbb{R}^d\rightarrow\mathbb{R}^d$ and
$\tilde{b}:\mathbb{R}^{2d}\rightarrow\mathbb{R}^d$ are two globally Lipschitz
continuous functions, and $(L_t)_{t\ge0}$ is an $\mathbb{R}^d$-valued pure jump
L\'evy process. The proof is also based on a novel distance function, which is
designed according to the distance of the marginals associated with the
constructed coupling process. Furthermore, by applying the coupling technique
above with some modifications, we also provide the propagation of chaos
uniformly in time for the corresponding mean-field interacting particle systems
with L\'evy noises in the standard $L^1$-Wasserstein distance as well as with
explicit bounds.
