  We consider a system of stochastic interacting particles in $\mathbb{R}^d$
and we describe large deviations asymptotics in a joint mean-field and
small-noise limit. Precisely, a large deviations principle (LDP) is established
for the empirical measure and the stochastic current, as the number of
particles tends to infinity and the noise vanishes, simultaneously. We give a
direct proof of the LDP using tilting and subsequently exploiting the link
between entropy and large deviations. To this aim we employ consistency of
suitable deterministic control problems associated to the stochastic dynamics.
