For CGCF you need a set designed for drop tuning, that has the gauge of the C increased to compensate for it being dropped. Using a conventional 4 string heavy set will result in a very floppy C.
Circle K Strings - Circle K Strings sell 'drop-tune' sets that are designed to have equal tension on each string in the drop tuning. There's a finely stepped choice of gauges here:
vStandard Drop-tuned 4 Strings.
I recommend the .118 .124 .130 .136 sets (extra light to medium heavy) depending on your tension preference.
Do you have the option of top-loading the string? The Circle K's have a short taperwound section of 1.625" that may not work with through-body stringing. There is no advantage to through-body stringing.
Alternatively you could design a custom set from single strings. Or use a 5 string set and discard the E string, but that is more expensive and a waste of a string.