I'd argue FDR was a populist. It just depends on what kind of populism and to what end.
You don't get modern discontent and populism (and the current president) without the expansive (at the expense of congress and the states) executive branch. You don't get the expansive executive branch without 1930s populists and FDR.
Obviously there's a lot more nuance and detail to it (the blame Nixon deserves being of specific note IMO) but the argument is there.
So I'd argue that both the means are bad and the end
FDR had the folksy charm to directly address the public and acquired a lot of power, but in most respects he seems the opposite of a populist. He was a party insider with a complex technocratic response to the Depression voters believed actually worked, not someone who spent his time picking fights and arguing he needed more power to defeat enemies (or making complete fantasy promises like Huey Lewis), he picked up a broad voter coalition including lots of minorities he neither scapegoated nor actually defended, and was a conventional moderate for the time on foreign policy and [future] culture war issues. He was more radical and centralised than previous Presidents when it came to economic policy and the role of the executive, but it wasn't a shouty type of radicalism, especially not compared with how socialists and fascists elsewhere addressed the subject of the Depression...