  The Copernican principle, the notion that we are not at a special location in
the Universe, is one of the cornerstones of modern cosmology and its violation
would invalidate the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metric,
causing a major change in our understanding of the Universe. Thus, it is of
fundamental importance to perform observational tests of this principle. We
determine the precision with which future surveys will be able to test the
Copernican principle and their ability to detect any possible violations. We
forecast constraints on the inhomogeneous Lema\^{\i}tre-Tolman-Bondi model with
a cosmological constant $\Lambda$ ($\Lambda$LTB), basically a cosmological
constant $\Lambda$ and cold dark matter ($\Lambda$CDM) model, but endowed with
a spherical inhomogeneity. We consider combinations of currently available data
and simulated Euclid data, together with external data products, based on both
$\Lambda$CDM and $\Lambda$LTB fiducial models. These constraints are compared
to the expectations from the Copernican principle. When considering the
$\Lambda$CDM fiducial model, we find that Euclid data, in combination with
other current and forthcoming surveys, will improve the constraints on the
Copernican principle by about $30\%$, with $\pm10\%$ variations depending on
the observables and scales considered. On the other hand, when considering a
$\Lambda$LTB fiducial model, we find that future Euclid data, combined with
other current and forthcoming data sets, will be able to detect Gpc-scale
inhomogeneities of contrast $-0.1$. Next-generation surveys, such as Euclid,
will thoroughly test homogeneity at large scales, tightening the constraints on
possible violations of the Copernican principle.
