  We study a simple model of N-component fermions with contact interactions
which describes fermionic atoms with N=2F+1 hyperfine states loaded into a
one-dimensional optical lattice. We show by means of analytical and numerical
approaches that, for attractive interaction, a quasi-long-range molecular
superfluid phase emerges at low density. In such a phase, the pairing
instability is strongly suppressed and the leading instability is formed from
bound-states made of N fermions. At small density, the molecular superfluid
phase is generic and exists for a wide range of attractive contact interactions
without an SU(N) symmetry between the hyperfine states.
