  Interferometric wavelength meters have attained frequency resolutions down to
the MHz range. In particular, Fizeau interferometers, which have no moving
parts, are becoming a popular tool for laser characterization and
stabilization. In this article, we characterize such a wavelength meter using
an ultra-stable laser in terms of relative frequency instability
$\sigma_y(\tau)$ and demonstrate that it can achieve a short-term instability
$\sigma_y(1 s) \approx 2{\times}10^{-10}$ and a frequency drift of order $10$
MHz/day. We use this apparatus to demonstrate frequency control of a
near-infrared laser, where a frequency instability below $3{\times}10^{-10}$
from 1 s to 2000 s is achieved. Such performance is for example adequate for
ions trapping and atoms cooling experiments.
