  We consider a free-standing metallic nanofilm with a predominant intersubband
paring which emerges as a result of the confinement in the growth direction. We
show that the Fermi wave vector mismatch between the subbands, detrimental to
the intersubband pairing, can be compensated by the non-zero center of mass
momentum of the Cooper pairs. This leads to the spontaneous appearance of the
intersubband Fulde-Ferrell (IFF) state, even in the absence of an external
magnetic field. Our study of the intrasubband pairing channel on the stability
of the IFF phase shows that the former strongly competes with the intersubband
pairing, which prohibits the coexistence of the two superconducting phases.
Interestingly, upon application of the magnetic field we find a transition to
an exotic mixed spin-singlet subband-triplet and spin-triplet subband-singlet
paired state. Finally, we discuss the possibility of existence of the IFF
pairing in novel superconducting materials.
