If you have GaussView, open the output file, view the structure, and then use the "Save as" option to save a .cif file. There may be other programs (e.g., OpenBabel) that can do the file conversion.
GaussView (at least the 6.0 version for Linux) does not support saving to cif. Also the 'convert' tool does not support this option. Although it would not make much sense, it is possible to convert log --> mol (with GV or molden) and then mol --> cif (with Mercury).
You are correct about the "save as" option -- it is better to use the formatted checkpoint file from Gaussian and convert it to a .cif using OpenBabel.
I've never done this specifically, but it appears that ase can do this conversion (https://wiki.fysik.dtu.dk/ase/ase/io/io.html). If the Gaussian file doesn't have unit cell information, presumably you would have to provide this. Should be very easy to code up using ase's read and write commands.