I will go out on a limb to say that as long as they were In the Gan (I guess until Motzei Shabbos) they didnt need shoes but once out of the Gan they needed shoes. Im guessing in the Gan the ground was soft and smooth but outside there was rough ground and thorns and whatnot due to the klalah that Hashem cursed the ground due to Adams aveirah.
I think I once quoted a T’shuvah in the Tzitz Eliezer here about whether or not shoes Halachically count as clothes (the precise topic was putting on galosh-covered shoes or whether that’s an issue of putting on two Begadim at once, I believe). Presumably the same would apply here. If shoes are clothes, then for sure they didn’t wear them. If shoes aren’t, then there’s no Hechre that I know of (maybe a Medrash somewhere refers to it; I definitely don’t recall one about it though).