  WASP-127b is one of the puffiest exoplanets found to date, with a mass only
$3.4$ Neptune masses, but a radius larger than Jupiter. It is also located at
the border of the Neptune desert, which describes the lack of highly-irradiated
Neptune-sized planets, and which remains poorly understood. Its large scale
height and bright host star make the transiting WASP-127b a valuable target to
characterise in transmission spectroscopy. We use combined EulerCam and TESS
light curves to recalculate the system's parameters. Additionally, we present
an in-depth search for sodium in four transit observations of WASP-127b,
obtained as part of the Hot Exoplanet Atmosphere Resolved with Transit
Spectroscopy (HEARTS) survey with the High Accuracy Radial velocity Planet
Searcher (HARPS) spectrograph. Two nights from this dataset were analysed
independently by another team, claiming a detection of sodium incompatible with
previous studies of data from both ground and space. We show that this large
sodium detection is actually due to contamination from telluric sodium
emissions and the low S/N in the core of the deep stellar sodium lines. When
properly accounting for these effects, the previous sodium signal is reduced to
an absorption of $0.46\pm0.20\%$ ($2.3\sigma$), which is compatible with
analyses of WASP-127b transits carried out with other instruments. We can fit a
Gaussian to the D2 line, however, the D1 line was not detected, indicating an
unusual line ratio if sodium exists in the atmosphere. Follow-up of WASP-127 at
both high-resolution and with high sensitivity will be required to firmly
establish the presence of sodium and analyse its line shape.
