  Beyond the standard cosmological model the late-time accelerated expansion of
the universe can be reproduced by the introduction of an additional dynamical
scalar field. In this case, the field is expected to be naturally coupled to
the rest of the theory's fields, unless a (still unknown) symmetry suppresses
this coupling. Therefore, this would possibly lead to some observational
consequences, such as space-time variations of nature's fundamental constants.
In this paper we investigate the coupling between a dynamical Dark Energy model
and the electromagnetic field, and the corresponding evolution of the fine
structure constant ($\alpha$) with respect to the standard local value
$\alpha_0$. In particular, we derive joint constraints on two dynamical Dark
Energy model parametrizations (the Chevallier-Polarski-Linder and Early Dark
Energy model) and on the coupling with electromagnetism $\zeta$, forecasting
future low-medium redshift observations. We combine supernovae and weak lensing
measurements from the Euclid experiment with high-resolution spectroscopy
measurements of fundamental couplings and the redshift drift from the European
Extremely Large Telescope, highlighting the contribution of each probe.
Moreover, we also consider the case where the field driving the $\alpha$
evolution is not the one responsible for cosmic acceleration and investigate
how future observations can constrain this scenario.
