The Yerushalmi (Nazir 9:3) records that the standard way of burying people is with their legs extended and their hands over their hearts. Elsewhere (Kilayim 9:3) it records how R Yirmeya asked to be laid on his side, as if ready to awake and greet the Mashiach, in his grave. The Bavli (BB 74a) describes how the Jews who died while wandering the desert for 40 years were sleeping on their backs.
The Tur (YD 362) writes:
ולדברי הכל נותנים המת על גביו ופניו למעלה והכי איתא בירושלמי יהבוני על גבי לא עומד ולא יושב ולא מונח ראשי בין ברכי אלא כאדם שהוא ישן
And according to everyone we lay the deceased down on his back with his face up, and so it says in the Yerushalmi [TTBOMK we don't have this exact line in our Yerushalmi -- AA]: Lay me on my back, not standing, not sitting, and not with my head between my knees, but rather as one who is sleeping.
The Shulchan Arukh (362:2) rules as well that the deceased should be laid as if sleeping on his back with his face up. The Shakh there (sk 2) writes that in a standing or sitting position would be "דרך גנאי", a disgraceful way of being buried.
It's hard to say burying someone in the fetal position would not fulfill the obligation of burial, but the traditional position seems to be strongly preferred.