RebE, good to hear from you! A git yohr! The problem here is that Adam could surely eat the fruit on Shabbos, but he would not be able to harvest it from the tree!
In fact, this explains why Hava & Nahash are talking touching the tree – a clear midrabonon on Shabbos.
In fact, the bigger problem is that Adam would not have been able to marry on Shabbos. We would not want him to stay single forever, right – first, he would be a half-a-man, effectively reducing humanity by 50%, but also we would all be bastards then.
So, he had to be married before Shabbos. And the rest was, as they say, “history”. What else do you expect from the isha?!