  Most massive stars reside in multiple systems that will interact over the
course of their lifetime. Classical Wolf-Rayet (WR) stars represent the final
end stages of stellar evolution at the upper-mass end. As part of a
homogeneous, magnitude-limited ($V\leq12$) spectroscopic survey of northern
Galactic WR stars, this paper aims to establish the observed and intrinsic
multiplicity properties of the early-type nitrogen-rich WR population (WNE). We
obtained high-resolution spectroscopic time series of the complete
magnitude-limited sample of 16 WNE stars observable with the 1.2 m Mercator
telescope at La Palma, typically providing a time base of about two to eight
years. We measured relative radial velocities (RVs) using cross-correlation and
used RV variations to flag binary candidates. Adopting a peak-to-peak RV
variability threshold of 50 km/s as a criterion found an observed multiplicity
fraction of 0.44$\pm$0.12. Using an updated Monte Carlo method with a Bayesian
framework, we calculated the three-dimensional likelihood for the intrinsic
binary fraction, the maximum period, and the power-law index for the period
distribution for the WNE population. We also re-derived multiplicity parameters
for the Galactic WC population. We found an intrinsic multiplicity fraction of
$0.56\substack{+0.20 \\ -0.15}$ for the parent WNE population. For the Galactic
WC population, we re-derive an intrinsic multiplicity fraction of
$0.96\substack{+0.04 \\ -0.22}$. The derived multiplicity parameters for the
WNE population are quite similar to those derived for main-sequence O binaries
but differ from those of the WC population. The significant shift in the WC
period distribution towards longer periods is too large to be explained via
expansion of the orbit due to stellar winds, and we discuss possible
implications of our results.

Solar and Stellar Astrophysics;Astrophysics of Galaxies