  We present near-infrared photometry and optical spectroscopy of very low-mass
stars and brown dwarf candidates in the Pleiades open cluster. The membership
status of these objects is assessed. Eight objects out of 45 appear to be
non-members. A search for companions among 34 very low-mass Pleiades members
(M$\le$0.09 M$_\odot$) in high-spatial resolution images obtained with the
Hubble Space Telescope and the adaptive optics system of the
Canada-France-Hawaii telescope produced no resolved binaries with separations
larger than 0.2 arcsec (a ~ 27 AU; P ~ 444 years). Nevertheless, we find
evidence for a binary sequence in the color-magnitude diagrams, in agreement
with the results of Steele & Jameson (1995) for higher mass stars. We compare
the multiplicity statistics of the Pleiades very low-mass stars and brown
dwarfs with that of G and K-type main sequence stars in the solar neighborhood
(Duquennoy & Mayor 1991). We find that there is some evidence for a deficiency
of wide binary systems (separation >27 AU) among the Pleiades very low-mass
members. We briefly discuss how this result can fit with current scenarios of
brown dwarf formation. We correct the Pleiades substellar mass function for the
contamination of cluster non-members found in this work. We find a
contamination level of 33% among the brown dwarf candidates identified by
Bouvier et al. (1998). Assuming a power law IMF across the substellar boundary,
we find a slope dN/dM ~ M^{-0.53}, implying that the number of objects per mass
bin is still rising but the contribution to the total mass of the cluster is
declining in the brown dwarf regime.
