Why does rabbinic literature identify France with Tzarfat? Tzarfat itself is mentioned only a few times, namely 'Ovadia 1:20, along with the only istance of Sepharad (which is identified with Spain) and Melachim 1:17:9-10.
Is this identification part of a general project of the rabbis using biblical place names for European regions? If so, what are their earliest references to these usages?
I am not sure it's an answer to your question, but I've heard a rabbi on youtube saying Tsarfat comes from the french baguette ( צר= narrow, straight + פת = bread = צרפת, straight bread, baguette ). I thought that was quite funny but it might actually be the origin of the word.
I don't know the earliest source but you might want to look at אגרת הרמב"ן לרבני צרפת The letter from the Ramban to the rabbis of "tzorfas"(France), where he defends the Rambam from the attacks of Rav Shlomo Petit and other Rabbonim who lived in Paris (where they subsequently burnt the Rambam Seforim).
He mentions רבותינו הצרפתים, תלמידיכם אנו ומימיכם אנו שותים that he is a student of the French rabbis the Baalei Tosfos (Rashi Rabbeinu Tam Ri Rav Yechiel and many others who lived all over france in Troyes, Ramerupt, Touques, Danpierre, Paris etc.) whom he quotes all over Shas thousands of times. (One can look up these names of Rabbis and places on wikipedia to confirm that these Rabbis came from what is known as France today)