Fanny Burney is often unfavourably compared to Jane Austen which I think is very unfair. In Evelina, some of the similarities are more prominent than in her other books (in terms of plot and milieu, at least) but I don't think it's helpful to approach this expecting another Pride & Prejudice.
Evelina has a tangled family history full of eloped marriages and abandonments: brought up by her clergy-man godfather, she has lived a sheltered life in the country until a family friend invites her to stay and Evelina makes her unexpected debut in London. There she send all the young men into a spin, and encounters her French grandmother who has plans of her own.
This is written in epistolary mode, with the majority of the letters being Evelina's own account of her doings. Burney is far bawdier that Austen and reminds me a little of Fielding, with Evelina as a more moral Tom Jones let loose on the big world with all her innocence. Her French grandmother, in particular, is a wonderful character with her bad English and her dodgy manners; as is the father of Evelina's best friend, who is one of the rudest men in literature.
We know there's going to be a happy ending from the start and there are no twists in the romance plot. But for something far breezier and bracing than Austen (who I love) this is highly recommended.