  The role played by environment in galaxy evolution is a current debate in
astronomy. The degree to which environment can alter, re-shape, or drive galaxy
evolution is a topic of discussion in both fronts, observations and
simulations. This paper analyses the gas metallicity gradients for a sample of
10 Fornax cluster galaxies observed with MUSE as part of the Fornax3D project.
Detailed maps of emission lines allowed a precise determination of gas
metallicity and metallicity gradients.
  The integrated gas metallicity of our Fornax cluster galaxies show slightly
higher metallicities (~0.045 dex) in comparison to a control sample. In
addition, we find signs of a mass and metallicity segregation from the center
to the outskirts of the cluster.
  By comparing our Fornax cluster metallicity gradients with a control sample
we find a general median offset of ~0.04 dex/Re, with 8 of our galaxies showing
flatter or more positive gradients.
  We find no systematic difference between the gradients of recent and
intermediate infallers when considering the projected distance of each galaxy
to the cluster center.
  To identify the origin of the observed offset in the metallicity gradients,
we perform a similar analysis with data from the TNG50 simulation. We identify
12 subhalos in Fornax-like clusters and compare their metallicity gradients
with a control sample of field subhalos. This exercise also shows a flattening
in the metallicity gradients for galaxies in Fornax-like halos, with a median
offset of ~0.05 dex/Re We also analyse the merger history, Mach numbers (M),
and ram pressure stripping of our TNG50 sample. We conclude that the observed
flattening in metallicity gradients is likely due to a combination of galaxies
traveling at supersonic velocities (M>1) that are experiencing high ram
pressure stripping and flybys.
