The genre of The French Lieutenant's Woman is confusing: it isn't a Victorian novel, although the first few chapters seem to nod at this genre, and the rest of the novel keeps up some pretense of belonging to the tradition. James R. Baker has called The French Lieutenant's Woman a "pseudo-historical" novel. It seems important to outline a few features of Victorian literature that Fowles then goes on to adopt, or distort.
Victorian novels tend to be quite earnest, and even didactic: they often come with a clear moral at the end. In tragedies, the characters end up badly (e.g., in most of Hardy's works), and lighter fiction of the period ends with marriages. The French Lieutenant's Woman breaks with this tradition by providing an ambiguous second ending, in which the characters are clearly different than they were at the start, and in Sarah's case happier, but Charles in the second ending is plunged into existential reflection, and there doesn't seem to be much closure for him - will he end up living happily or not? It would be difficult to come up with a moral for the whole novel; Fowles seems to be commenting on the Victorian age and the nature of fiction more than offering moral judgments on the characters and the plot line.
Victorian fiction tended to be heavily plotted and described in a realistic way, with plenty of description of the emotional states of the characters as well as the settings and the time period. The French Lieutenant's Woman has some plot, but also spends a lot of time in the various characters' minds - including the narrator's - in a way that doesn't advance the story very much.
Fowles' novel certainly does describe contemporary society, which was a common feature of Victorian novels - the Victorians loved reading about themselves. Fowles includes plenty of details about everyday life in 1867, which was a common feature of fiction written in that time period. He also deals with some of the biggest issues discussed in fiction at the time: evolution, industrialism, poverty, and women's rights.
Visual imagery is a hallmark of Victorian fiction, more so than any type of novels that had gone before. Victorian novels imitated poetry in this sense, focusing on depicting the setting of the story in a highly visual way - although the novels tended to use more realistic detail and a little less figurative language. Fowles uses a lot of imagery in his novel - religious imagery and natural imagery, to name just two types.
Victorian novels tend to have a crowded cast of characters but a clear hero or heroine, and The French Lieutenant's Woman follows this model to a degree. We have the main pairing of Sarah and Charles, but side characters play important roles: Ernestina, Mary, Sam, Mr. Freeman, Mrs. Poulteney, and others all have a part to play.
The main break from the Victorian novel is the narrative voice in The French Lieutenant's Woman, which is incredibly postmodern and ironic, and prevents us from taking the novel too seriously.