Disclaimer: I am not a student of comp lit, but I was planning to pursue it (applied last year) so I took some time to really learn about the field.
Learning Turkish will definitely help you in Comp Lit - in fact it will hurt you if don't have multiple languages. However, you already have Persian and French under your belt so while learning Turkish is nice, you've already won the battle.
In general, language combinations are totally up to you in Comp Lit, but you have to be ale to connect them somehow -- whether that is a shared literary movement, did a famous French author live in Turkey and that informed their writings, do the languages share politics, borders, etc. You need to be able to connect them somehow. This is crucial for you to be apple to explain in your applications. Funny enough a friend of mine is getting her PhD in Comp Lit and her languages are Turkish and French - but it is uncommon. She said it is both extremely challenging, but extremely impressive because it's not common. She mentioned that it adds to her stress a little bit because it's only impressive if she does it well. I think her foci are memory, trauma and genocide connecting the languages). TLDR: Any language combination is good as long as you can connect them.
For linguistics, you don't need to speak another language to study it. Some of the most famous linguists like Noam Chomsky don't speak any languages other than English. So knowing other languages will certainly help you as a linguist (and make you stand out in your apps), but it isn't required in the way Comp Lit requires languages.