Akum Sheba al Bas Yisrael havlad kasher. (Kid. 71b , Yevamos 23a & 45a). Most rishonim say the child is a full Jew. However, Rashi in Kiddushin and Tosfos Bechoros 47 hold the kid is kosher in that he isn't a mamzer, but he is is asur lavo bekahal until he undergoes geirus. See this article from Rav Aharon Soloveichik in Hapardes 23 (1949), where explains this shita. Begins here at bottom, continues, 2, 3, and 4.
Also see Rabi Akiva Eiger on Shulchan Aruch Y.D. 266, Se'if 12 who mentions that to this shita you would not do a bris on this kid on shabbos, presumably since he's not Jewish (but according to Rav Aharon he is Jewish, he just is asur lavo bekahal so you would do the bris on shabbos).