  Millisecond pulsars (MSPs) represent nearly half of the more than 160
currently known $\gamma$-ray pulsars detected by the Large Area Telescope on
the \textit{Fermi} satellite, and a third of all known MSPs are seen in
$\gamma$ rays. The least energetic $\gamma$-ray MSPs enable us to probe the
so-called deathline for high-energy emission, i.e., the spin-down luminosity
limit under which pulsars (PSRs) cease to produce detectable high-energy
radiation. Characterizing the MSP luminosity distribution helps to determine
their contribution to the Galactic diffuse $\gamma$-ray emission. We made use
of the high-quality pulsar timing data recorded at the Nan\c{c}ay Radio
Telescope over several years to characterize the properties of a selection of
MSPs. For one of the pulsars, the dataset was complemented with Westerbork
Synthesis Radio Telescope observations. The rotation ephemerides derived from
this analysis were also used to search the LAT data for new $\gamma$-ray MSPs.
For the MSPs considered in this study, we obtained new transverse proper motion
measurements or updated the existing ones, and placed new distance constraints
for some of them, with four new timing parallax measurements. We discovered
significant GeV $\gamma$-ray signals from four MSPs, i.e., PSRs J0740+6620,
J0931$-$1902, J1455$-$3330, and J1730$-$2304. The latter is now the least
energetic $\gamma$-ray pulsar found to date. Despite the improved $\dot E$ and
$L_\gamma$ estimates, the relationship between these two quantities remains
unclear, especially at low $\dot E$ values.
