  Accurate polarimetric calibration of the radio pulse profiles from pulsars is
crucial for studying their radiation properties at these wavelengths.
Inaccurate calibration can also distort recorded pulse profiles, introducing
noise in time of arrival (TOA) data and thus degrading pulsar timing analyses.
One method for determining the full polarimetric response of a given telescope
is to conduct observations of bright polarized pulsars over wide ranges of
parallactic angles, to sample different orientations of their polarization
angle and determine the cross-couplings between polarization feeds. The
Nan\c{c}ay decimetric Radio Telescope (NRT) is a 94m equivalent meridian
telescope, capable of tracking a given pulsar for approximately one hour around
transit. In November 2019, we began conducting regular observations of the
bright and highly linearly polarized pulsar PSR~J0742$-$2822, in a special mode
where the feed horn rotates by $\sim 180^\circ$ over the course of the one hour
observation, mimicking wide parallactic angle variations and enabling us to
determine the polarimetric response of the NRT at 1.4~GHz. The improved
polarimetric response of the NRT as determined from these observations was
applied to observations of a selection of MSPs with published polarimetric
properties. We find that the new polarimetric profiles and polarization
position angles are consistent with previous findings, unlike NRT polarimetric
results obtained with the previously used method of calibration. The analysis
of timing data on J1730$-$2304, J1744$-$1134, and J1857+0953 shows that the new
calibration method improves the quality of the timing, and the Matrix Template
Matching (MTM) method proves very effective at reducing noise from imperfect
calibration. For pulsars with sufficient degrees of polarization, the MTM
method appears to be the preferred method for extracting TOAs from NRT
observations.
