It looks to me that you want to output lines where the first field, in a comma-separated list of fields, ends with 'F'
If you don't care about listing which .gz file the lines come from, or which file within the gzipped file -- that is, you just want the lines listed -- you don't even have to gunzip the .gz files first, that way you won't have to re-zip them.
zcat file.gz | awk -F, '$1 ~ /F$/'
For every file in the current directory tree, use a find with xargs. This example limits it to only the current directory, but just leave out the "-maxdepth 1" to get the whole directory tree
find . -maxdepth 1 -name \*.gz -print0 | xargs -0 zcat | awk -F, '$1 ~ /F$/'
This says to find files that end in ".gz" and write their names with a NUL terminator (the 0 in -print0), pipe that output through xargs which will pick the list apart based on NUL chacracters (the "-0" arg) and run zcat on the files. Pipe that output through your awk command and you'll get the relevent lines written out.