Jackson hated central banking, so he never belonged on FRNs in the first place.
It's more important to look at WHY Jackson hated what he did rather than the specific things he hated. In other words, Jackson did not have this principled attachment to small government that we for some reason attach to him. It is pure coincidence (based on how developed our economy was/is, the global competition, etc.) that a centralized government/economy benefited American businesses back then and does not today. Jackson was much more tied to his hatred of what was in essence the ancestor of trickle down economics than he was to his supposed love of states' rights and small government, and he'd be hootin' and hollerin' about saving the social safety net, rejecting free trade (an ideologically consistent yet "opposite" view from his actual stance in the 1800s), redistributing wealth and all that jazz today.
I digress.