But Satan was a fallen angel, so how did he come to take the form of a snake in Gen 3:1?

There are two ways to make sense of this theory. One is the common way: Satan is a spiritual being, like angels, which might at least sometime be spatio-temporally located, but which lack a body. Indeed, sometimes, perhaps they lack any spatio-temporal location (more on that further down). In the same way that demons could inhabit the bodies of pigs (see Matt. 8:30-33), presumably Satan could inhabit (or otherwise animate) the body of a snake, and even make it speak, or seem to speak. The other theory begins from the observation that the “seraphim” (a kind of angelic being, but probably not the sort of entity normally called an “angel”) were actually flying serpents, since the Hebrew word, seraphim, meant (at least in one sense) “serpents.” So the serpent might have simply been a seraph,and then maybe the suggestion, according to the theory, is that Satan was originally such a seraph. The three enormous problems with this are (a) when the heavenly seraphim are actually described in Isaiah 6:1-8, they are described as beings with six wings, human appendages, and voices, and certainly not flying snakes; (b) Satan and other deadly and evil things are called “serpents,” and it seems unlikely that the visual appearance of any holy thing in God’s presence would be associated with such a symbol of death; and to really clinch the matter, (c) Ezek 28:14 has a figure called “Lucifer,” often taken as referring to Satan, described not as a seraph but as a cherub, and nobody thinks cherubim were serpentine. So I suggest we stick with the common theory.