Well the avast updates don't use any browser, so they aren't responsible for any spike in firefox. I don't see this on my system and firefox is my default browser.
What are you doing with firefox at that time ?
If it is just starting and you have lots of add-ons, etc. those plus the various files that firefox loads can use a fair amount of CPU for a period of time.
Unfortunately we know nothing about your system, OS, CPU, RAM, etc. ?
What is your connection method, dial-up/broadband ?