Fabienne is Butch's adorable girlfriend, who just wants some blueberry pancakes and maybe some pie—oh, and a potbelly, which we're pretty sure comes free with the first two. With her naiveté and innocence, she's a sharp contrast to the murderous, double crossing Butch. She knows that they're in danger but Butch never goes into the details. Still, she's willing to follow him out of town and maybe out of the country.
Fabienne seems to adore Butch except when he teases her or loses his temper. One theory about Fabienne is that she's pregnant. Evidence? Telling Butch about imagining herself with a pot-belly, where everything about you is the same except for a big belly; her insatiable appetite for someone so petite, with a specific craving for blueberry pancakes; her mentioning to Butch that she has something to tell him. (Source)
Fabienne's character makes Butch a more complex guy. She's not the kind of girlfriend you'd expect of someone like him—not tough, not glamorous. She shows us Butch's softer side. He gets furious with her for forgetting his watch back at their apartment, but after he blows up, he calms down, apologizes and comforts her.