The only fuchsia I have tried from seed is the F. procumbens, a 2" tall groundcover. I makes nice big red berries late summer/fall. I just pick berries, which are the size of a grape, put them in a bowl of water, then break them up with my fingers, then I carefully run water over them and wash away the flesh, the seeds are more dense and tend to stay in the bottom of the bowl. it takes about 5 minutes to get them clean. then I dry them, I have done this in a bowl, and on typing paper. Either way they stick as they dry and have to be rubbed off. I continue drying them in a dish on the kitchen counter until they are really dry and not sticky, then package them up.
I have sprouted them in seed starting mix on the kitchen counter, and using the "Deno Method" of folded moist paper towel in a loose unsealed baggie on the counter. They do not need any kind of special treatment and sprout rapidly. I have never tried other fuchsias, I assume they would be similar. BTW, if you have not put any poisons on them the berries are edible!