[Update for those who might encounter similar issue in the future]
After talking to my counselor and UC Reps it was concluded that I retake the HCOM 100 course at CSUF and replace the F with a better grade that way I would be in good standing there as well. The UC’s do count the overall GPA however they look at the trend of the student’s grades. Nevertheless, in order to increase the GPA, the best solution is to retake the class at the same institution and replace the failing grade.