Franklin County is home to Frankfort, Kentucky's capital city. State capitols usually are more Democratic than their states as a whole, due to possessing both a substantial government workforce and a notable minority population, as well as large numbers of younger, college-educated voters. Denver, Colorado, Atlanta, Georgia, Santa Fe, New Mexico, and Austin, Texas are examples of this.
Nevertheless, Trump won Franklin County with a plurality both times. Frankfort is a relatively small and more conservative city, and I've noticed that the smaller a state capitol is, the more likely it is to be Republican-Carson City, Nevada, Jefferson City, Missouri, and Cheyenne, Wyoming exemplify this.
Springfield, IL, is the clearest remaining exception to this pattern. It tends to vote Democratic today, but by much smaller margins than similar-sized cities in the downstate (Biden got about 55% there, compared to 61% each in Peoria and Rockford), and its environs are firmly Republican. Sangamon County has only voted Democratic three times since 1936, although Biden came within five points: 1964, 1992, and 2008. Tammy Duckworth, in the midst of a massive overperformance downstate, only won it by about a point in 2016. I don't know enough about the city of Springfield to say much on why it remains fairly conservative even compared to demographically similar state capitals, but being in an ancestrally Unionist/Republican region and lacking a major higher education presence is probably much of the reason.