  We present precise measurements of the quantum defects of cesium $n$F$_J$
Rydberg levels. We employ high-precision microwave spectroscopy of
$(n+2)\mathrm{D}_{5/2}\rightarrow n\mathrm{F}_{5/2,7/2}$ transitions for $n=45$
to 50 in a cold-atom setup. Cold cesium $(n+2)$D$_{5/2}$ atoms, prepared via
two-photon laser excitation, are probed by scanning weak microwave fields
interacting with the atoms across the $n\mathrm{F}_{5/2,7/2}$ resonances.
Transition spectra are acquired using state-selective electric-field ionization
and time-gated ion detection. Transition-frequency intervals are obtained by
Lorentzian fits to the measured spectral lines, which have linewidths ranging
between 70~kHz and 190~kHz, corresponding to about one to three times the
Fourier limit. A comprehensive analysis of relevant line-shift uncertainties
and line-broadening effects is conducted. We find quantum defect parameters
$\delta_{0}(\mathrm{F}_{5/2})=0.03341537(70)$ and
$\delta_{2}(\mathrm{F}_{5/2})=-0.2014(16)$, as well as
$\delta_{0}(\mathrm{F}_{7/2})=0.0335646(13)$ and
$\delta_{2}(\mathrm{F}_{7/2})=-0.2052(29)$, for $J=5/2$ and $J=7/2$,
respectively. Fine structure parameters $A_{FS}$ and $B_{FS}$ for Cs
$n{\rm{F}}_J$ are also obtained. Results are discussed in context with previous
works, and the significance of the results is discussed.
