The closest you can get is to use the French equivalent of the name's origin, which is likely "Julienne" (pronounced "zhoo-lyen").
Julienne is a common French name, meaning "youthful" or "downy-bearded". It's a feminine form of "Julien", a name with strong roots in French culture.
However, it's important to note that Julienne is a distinct name from "Jillian" and might not be perceived as a direct equivalent. Ultimately, the best way to refer to someone named Jillian in French would be to simply use their name as is.