EROS has been monitoring few million stars in the Magellanic clouds, as well as toward the Galactic bulge and spiral arms since 1996, to search for microlensing events. In this paper, we present briefly the EROS setup and scientific program and discuss the results obtained from our observations in four directions in the Galactic plane, away from the bulge. Seven light curves, out of 9.1 million stars observed in these directions show luminosity variations interpreted as due to microlensing. The averaged estimated optical depth tau = 0.45 +0.24 -0.11 is compatible with expectations from simple Galactic models. Nonetheless a small excess of short time-scale events may be present in the direction closest to the Galactic center.