  The physical mechanisms driving star formation (SF) in galaxies are still not
fully understood. Tidal dwarf galaxies (TDGs), made of gas ejected during
galaxy interactions, seem to be devoid of dark matter and have a near-solar
metallicity. The latter makes it possible to study molecular gas and its link
to SF using standard tracers (CO, dust) in a peculiar environment. We present a
detailed study of a nearby TDG in the Virgo Cluster, VCC 2062, using new
high-resolution CO(1--0) data from the Plateau de Bure, deep optical imaging
from the Next Generation Virgo Cluster Survey (NGVS), and complementary
multiwavelength data. Until now, there was some doubt whether VCC 2062 was a
true TDG, but the new deep optical images from the NGVS reveal a stellar bridge
between VCC 2062 and its parent galaxy, NGC 4694, which is clear proof of its
tidal origin. Several high-resolution tracers (\halpha, UV, 8~\mi, and 24~\mi)
of the star formation rate (SFR) are compared to the molecular gas distribution
as traced by the CO(1-0). Coupled with the SFR tracers, the NGVS data are used
with the CIGALE code to model the stellar populations throughout VCC 2062,
yielding a declining SFR in the recent past, consistent with the low \halpha/UV
ratio, and a high burst strength. HI emission covers VCC 2062, whereas the CO
is concentrated near the HI maxima. The CO peaks correspond to two very
distinct regions: one with moderate SF to the NE and one with only slightly
weaker CO emission but with nearly no SF. Even where SF is clearly present, the
SFR is below the value expected from the surface density of the molecular and
the total gas as compared to spiral galaxies and other TDGs. After discussing
different possible explanations, we conclude that the low surface brightness is
a crucial parameter to understand the low SFR.
