I actually had a separate user email me directly for this exact same problem. In their case they needed the lon/lats in binary files on disk. I'm not familiar with the FCI reader's defaults so it is possible these arrays are flipped, but this is the basic code:
from satpy import Scene
from glob import glob
scn = Scene(reader="fci_l1c_nc", filenames=glob("/data/satellite/fci/uncompressed/RC0067/*BODY*"))
scn.load(["vis_04"])
lons, lats = scn["vis_04"].attrs["area"].get_lonlats()
lons.tofile("fci_vis04_lons_f64.dat")
lats.tofile("fci_vis04_lats_f64.dat")
Dave