Fran is kind of similar to Seinfeld's Elaine, except she's a chain smoking alcoholic who has given up on any dream of "normality" in her life. Her best friend is Bernard, the grumpy drunk who owns "Black Books". Occasionally Fran will try and connect with other people, family or old school friends, but this always ends badly and she ends up back with Bernard and Manny, getting pissed on cheap red wine and complaining about everything.
While despising Bernard, it seems that Fran also relates to him quite a bit, hence their long friendship. Manny is the "normal" character of the show. He spouts a fair amount of crazy things, but he's generally really happy and chirpy. Fran likes Manny and supports him when Bernard is continually using and berating him, but Fran will also use Manny's eagerness in her own way.
In the first season of Black Books Fran owned a gift store that was next to Black Books, but she went out of business and is unemployed in season two. She is a strong, relatable woman who doesn't buy into "normal life" in any way. If anything, the idea of settling down with a husband and kids completely infuriates her.
All three characters in Black Books are essential to the show being so fantastic, but I find Fran to be the most relatable of the three.