  Using $e^+e^-$ collision data corresponding to an integrated luminosity of
7.33 ${\rm fb^{-1}}$ recorded by the BESIII detector at center-of-mass energies
between 4.128 and 4.226 ${\rm GeV}$, we present an analysis of the decay
$D_{s}^{+} \to f_{0}(980)e^{+}\nu_{e}$ with $f_{0}(980) \to \pi^{+}\pi^{-}$,
where the $D_s^+$ is produced via the process $e^+e^- \to
D_{s}^{*\pm}D_{s}^{\mp}$. We observe the $f_{0}(980)$ in the $\pi^+\pi^-$
system and the branching fraction of the decay $D_{s}^{+} \to
f_{0}(980)e^{+}\nu_{e}$ with $f_0(980)\to\pi^+\pi^-$ is measured to be $(1.72
\pm 0.13_{\rm stat} \pm 0.10_{\rm syst}) \times10^{-3}$, where the
uncertainties are statistical and systematic, respectively. The dynamics of the
$D_{s}^{+} \to f_{0}(980)e^{+}\nu_{e}$ decay are studied with the simple pole
parameterization of the hadronic form factor and the Flatt\'e formula
describing the $f_0(980)$ in the differential decay rate, and the product of
the form factor $f^{f_0}_{+}(0)$ and the $c\to s$ Cabibbo-Kobayashi-Maskawa
matrix element $|V_{cs}|$ is determined for the first time to be
$f^{f_0}_+(0)|V_{cs}|=0.504\pm0.017_{\rm stat}\pm0.035_{\rm syst}$.
