In Howard Zinn's A People's History of the United States, what does Zinn see as FDR's role in events?

Zinn essentially accepts the familiar narrative that Franklin Roosevelt was the architect of the New Deal, and he stresses the president's role in preserving capitalism by "stabilizing the system." Zinn does not deny that the New Deal made major reforms, far beyond anything the federal government contemplated doing before. However, he stresses that the New Deal did very little (by design) to fix the structures that led to the Great Depression in the first place:

When the New Deal was over, capitalism remained intact. The rich still controlled the nation's wealth, as well as its laws, courts, police, newspapers, churches, colleges. Enough help had been given to enough people to make Roosevelt a hero to millions, but the same system that had brought depression and crisis . . . remained.

Zinn's argument is that this was by design. FDR was never the "class traitor" his enemies accused him of being, and he refused to alienate the Southern Democrats that formed part of his coalition.
In the final analysis, the fundamental goal of the New Deal was to alleviate class tensions that emerged as a result of the Depression and of injustice in the American economic system in general. The Wagner Act, for example, which is often hailed as the "Magna Carta of labor" because it guaranteed the right of unions to organize and engage in collective bargaining, is framed as an attempt to bring about "the stability of commerce."
In short, FDR was more interested in preserving capitalism by forestalling radical change than in promoting it.

Howard Zinn, in A People's History of the United States, writes that Franklin Roosevelt's main goal in response to economic crisis was to re-organize the economy to overcome the crisis and stabilize capitalism. Zinn does acknowledge that the National Recovery Act (NRA) provided some concessions to the lower classes and resulted in socially beneficial outcomes (for example, creating jobs, modernizing poor regions, providing some social security, and building public housing). However, overall, these policies and reforms were limited and acted as preventive measures against popular rebellion (the period witnessed social upheavals as labour unions organized and led large strikes). To stabilize the system, New Deal policies sought to manage labour through state-managed partnerships with big business and industry. These measures, in Zinn's view, aimed to generate economic recovery in ways that favored big business and consolidated their powers through statist means.