Fluorine is going to make up for a lack of carbon? Where are you going to find the fluorine? There is 4800 times as much carbon in the universe as fluorine. It might be possible for life forms to metabolize free fluorine, carbon compounds like paraffin are stable with hydrogen fluoride which can be seen as a solvent gas but the rarity of fluorine and it's reactivity pretty much insure that free fluorine would not persist in an environment.
Then you have the problems of just how much fluorine there would have to be on a planet for free fluorine and fluorine compounds to exist. On the Earth we have oxygen, the entire earth is dominated by oxidized chemicals, rocks, and minerals. Free oxygen couldn't exist in any significant amounts without everything on the Earth being saturated by oxygen. The same would have to happen for any planet dominated by fluorine but the key is that oxygen is more abundant than fluorine, 8800 times as abundant as fluorine to be exact.
Fluorine is simply too rare and reactive as an element to have fluorine play a role similar to oxygen or in combination with carbon to replace any of the major players in life as we know it.
https://en.wikipedia.org/wiki/Origin_and_occurrence_of_fluorine