  We construct families of fundamental, dipole, and tripole solitons in the
fractional Schr\"{o}dinger equation (FSE)\ incorporating self-focusing cubic
and defocusing quintic terms modulated by factors $\cos ^{2}x$ and $\sin^{2}x$,
respectively. While the fundamental solitons are similar to those in the model
with the uniform nonlinearity, the multipole complexes exist only in the
presence of the nonlinear lattice. The shapes and stability of all the solitons
strongly depend on the L\'{e}vy index (LI)\ that determines the FSE
fractionality. Stability areas are identified in the plane of LI and
propagation constant by means of numerical methods, and some results are
explained with the help of an analytical approximation. The stability areas are
broadest for the fundamental solitons and narrowest for the tripoles.
